Relevant bibliographies by topics / Differential geometry – Global differential geometry – Global differential geometry

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Differential geometry – Global differential geometry – Global differential geometry'

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Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Differential geometry – Global differential geometry – Global differential geometry"

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Banchoff, Thomas F., and S. S. Chern. "Global Differential Geometry." American Mathematical Monthly 98, no. 7 (1991): 669. http://dx.doi.org/10.2307/2324949.

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Banchoff, Thomas F. "Global Differential Geometry. Editor, S. S. Chern." American Mathematical Monthly 98, no. 7 (1991): 669–71. http://dx.doi.org/10.1080/00029890.1991.11995775.

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Huhtanen, Marko. "Differential geometry of matrix inversion." MATHEMATICA SCANDINAVICA 107, no. 2 (2010): 267. http://dx.doi.org/10.7146/math.scand.a-15155.

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Essentially, there exists just the dimension segregating (square) matrix subspaces. In view of algebraic operations, this quantity is not particularly descriptive. For differential geometric information on matrix inversion, the second fundamental form is found for the set of inverses of the invertible elements of a matrix subspace. Several conditions for this form to vanish are given, such as being equivalent to a Jordan subalgebra. Global measures of curvature are introduced in terms of an analogy of the Nash fiber.
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Park, F. C. "Optimal Robot Design and Differential Geometry." Journal of Mechanical Design 117, B (1995): 87–92. http://dx.doi.org/10.1115/1.2836475.

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In this article we survey some recent developments in optimal robot design, and collect some of the differential geometric approaches into a general mathematical framework for robot design. The geometric framework permits a set of coordinate-free definitions of robot performance that can be optimized for designing both open- and closed-chain robotic mechanisms. In particular, workspace volume is precisely defined by regarding the rigid body motions as a Riemannian manifold, and various features of actuators, as well as inertial characteristics of the robot, can be captured by the suitable selection of a Riemannian metric in configuration space. The integral functional of harmonic mapping theory also provides a simple and elegant global description of dexterity.
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Park, F. C. "Optimal Robot Design and Differential Geometry." Journal of Vibration and Acoustics 117, B (1995): 87–92. http://dx.doi.org/10.1115/1.2838681.

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In this article we survey some recent developments in optimal robot design, and collect some of the differential geometric approaches into a general mathematical framework for robot design. The geometric framework permits a set of coordinate-free definitions of robot performance that can be optimized for designing both open- and closed-chain robotic mechanisms. In particular, workspace volume is precisely defined by regarding the rigid body motions as a Riemannian manifold, and various features of actuators, as well as inertial characteristics of the robot, can be captured by the suitable selection of a Riemannian metric in configuration space. The integral functional of harmonic mapping theory also provides a simple and elegant global description of dexterity.
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Simon, Udo. "Global uniqueness for ovaloids in Euclidean and affine differential geometry." Tohoku Mathematical Journal 44, no. 3 (1992): 327–34. http://dx.doi.org/10.2748/tmj/1178227299.

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Hale, J. K., and W. Z. Huang. "Global Geometry of the Stable Regions for Two Delay Differential Equations." Journal of Mathematical Analysis and Applications 178, no. 2 (1993): 344–62. http://dx.doi.org/10.1006/jmaa.1993.1312.

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CAZALS, FRÉDÉRIC, and MARC POUGET. "DIFFERENTIAL TOPOLOGY AND GEOMETRY OF SMOOTH EMBEDDED SURFACES: SELECTED TOPICS." International Journal of Computational Geometry & Applications 15, no. 05 (2005): 511–36. http://dx.doi.org/10.1142/s0218195905001816.

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The understanding of surfaces embedded in E3 requires local and global concepts, which are respectively evocative of differential geometry and differential topology. While the local theory has been classical for decades, global objects such as the foliations defined by the lines of curvature, or the medial axis still pose challenging mathematical problems. This duality is also tangible from a practical perspective, since algorithms manipulating sampled smooth surfaces (meshes or point clouds) are more developed in the local than the global category. As a prerequisite for those interested in the development of algorithms for the manipulation of surfaces, we propose a concise overview of core concepts from differential topology applied to smooth embedded surfaces. We first recall the classification of umbilics, of curvature lines, and describe the corresponding stable foliations. Next, fundamentals of contact and singularity theory are recalled, together with the classification of points induced by the contact of the surface with a sphere. This classification is further used to define ridges and their properties, and to recall the stratification properties of the medial axis. Finally, properties of the medial axis are used to present sufficient conditions ensuring that two embedded surfaces are ambient isotopic. From a theoretical perspective, we expect this survey to ease the access to intricate notions scattered over several sources. From a practical standpoint, we hope it will be useful for those interested in certified approximations of smooth surfaces.
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Malta, Iaci, Nicolau C. Saldanha, and Carlos Tomei. "Morin singularities and global geometry in a class of ordinary differential operators." Topological Methods in Nonlinear Analysis 10, no. 1 (1997): 137. http://dx.doi.org/10.12775/tmna.1997.026.

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SARDANASHVILY, G. "GEOMETRY OF CLASSICAL HIGGS FIELDS." International Journal of Geometric Methods in Modern Physics 03, no. 01 (2006): 139–48. http://dx.doi.org/10.1142/s0219887806001065.

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In gauge theory, Higgs fields are responsible for spontaneous symmetry breaking. In classical gauge theory on a principal bundle P, a symmetry breaking is defined as the reduction of a structure group of this principal bundle to a subgroup H of exact symmetries. This reduction takes place if and only if there exists a global section of the quotient bundle P/H. It is a classical Higgs field. A metric gravitational field exemplifies such a Higgs field. We summarize the basic facts on the reduction in principal bundles and geometry of Higgs fields. Our goal is the particular covariant differential in the presence of a Higgs field.
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Dissertations / Theses on the topic "Differential geometry – Global differential geometry – Global differential geometry"

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Pouget, Marc. "Geometry of surfaces : from the estimation of local differential quantities to the robust extraction of global differential features." Nice, 2005. http://www.theses.fr/2005NICE4052.

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Ce travail de recherche porte sur les aspects géométriques des mathématiques, de l’informatique et applications. Ce travail est fortement motivé par des applications telles que la conception assistée par ordinateur, l’imagerie médicale, le calcul scientifique et la simulation ou encore la réalité virtuelle et le multimédia. Cette thèse propose une analyse de la géométrie des surfaces tant d’un point de vue local que global. D’un point de vue local, le problème est l’estimation de la normale, des courbures et quantités d’ordre supérieur à partir d’une surface lise échantillonnée. D’un point de vue global, nous analysons les lignes d’extrême de courbure sur une surface, appelées ridges. D’une part, une méthode d’estimation des quantités différentielles locales avec ajustement d’un polynôme est étudiée : les propriétés de convergence sont établies et un algorithme est proposé et implémenté. D’autre part, des algorithmes sont développés pour le calcul de la topologie des ridges pour des surfaces discrétisées par un maillage ou paramétrées. Des conditions précises d’échantillonnage ainsi qu’un algorithme certifié sont données pour le cas d’une surface discrétisée par un maillage. Dans le cas d’une surface paramétrée, une équation implicite des ridges est calculée dans le domaine de paramétrage et les singularités sont analysées. Pour une paramétrisation polynomiale, ces équations sont aussi polynomiales et des méthodes spécifiques de calcul formel sont développées pour calculer la topologie de la courbe singulière des ridges<br>This research work relates to the geometrical aspects of mathematics, computer sciences and applications. This work is motivated by applications such as computer aided design, medical imaging, scientific computations and simulations or also virtual reality and multimedia. This thesis proposes an analysis of some local as well as global topics of the geometry of surfaces. From a local point of view, the problem is the estimation of the normal, the curvatures and quantities of higher order from points sampled on a smooth surface. From a global point of view, we analyze the lines of extreme curvature on surfaces, called ridges. On the one hand, a method for the estimation of local differential quantities with polynomial fitting is studied : the properties of convergence are established and an algorithm is proposed and implemented. On the other hand, algorithms are developed for the computation of the topology on the ridges for surfaces discretized by a mesh or parameterized. Precise conditions of sampling as wel as certified algorithm are given in the case of a surface, an implicit equation of the ridges is derived in the parametric domain and the singularities are analyzed for a polynomial parameterization. The equations are also polynomial, and specific methods of computer algebra are developed to compute the topology on the singular curve of the ridges
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Stewart, Chris G. "Incorporating global information into local nonlinear controllers." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/41900.

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Hitomi, Eduardo Eizo Aramaki 1989. "Equações parabólicas quase lineares e fluxos de curvatura média em espaços euclidianos." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306218.

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Orientador: Olivâine Santana de Queiroz<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-27T03:06:43Z (GMT). No. of bitstreams: 1 Hitomi_EduardoEizoAramaki_M.pdf: 5800906 bytes, checksum: 04b93921a20d8ab0f71d4977b9e93e73 (MD5) Previous issue date: 2015<br>Resumo: Nesta dissertação realizamos um estudo sobre o fluxo de curvatura média em espaços Euclidianos sob as perspectivas analítica e geométrica. Tratamos inicialmente da existência e regularidade de soluções em tempos pequenos de equações parabólicas quase lineares de segunda ordem em variedades Riemannianas, o que é essencial para garantirmos a existência de uma solução suave em tempo pequeno do fluxo de curvatura média. Em uma segunda parte, passamos a alguns resultados sobre o comportamento no intervalo maximal de existência de uma solução suave da hipersuperfície em evolução, por meio de equações das componentes geométricas associadas e de Princípios de Máximo. Próximo desse tempo maximal, analisamos a formação de singularidades do Tipo I por meio da Fórmula de Monotonicidade de Huisken e de rescalings, e do Tipo II por meio de uma técnica de blow-up devida a Hamilton. Em especial, reservamos o caso de curvas a um capítulo a parte e apresentamos resultados clássicos da teoria de curve-shortening flows<br>Abstract: In this dissertation we study the mean curvature flow in Euclidean spaces from the analytic and geometric point of view. We deal initially with short-time existence and regularity of a solution for second order quasilinear parabolic equations on Riemannian manifolds, which is essential to guarantee the short-time existence of a smooth solution to the mean curvature flow. In a second part, we present some results concerning the behavior of the evolving hypersurface close to the maximal time of existence of a smooth solution, by means of Maximum Principles and evolution equations of the associated geometric components. Close to this maximal time, we analyse the formation of singularities of Type I by means of rescalings and Huisken's Monotonicity Formula, and of Type II by means of a blow-up technique due to Hamilton. In particular, we reserve the case of curves to a separate chapter, where we present some classical results in curve-shortening flow theory<br>Mestrado<br>Matematica<br>Mestre em Matemática
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Paula, Pedro Manfrim Magalhães de 1991. "Consequências geométricas associadas à limitação do tensor de Bakry-Émery-Ricci." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306950.

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Orientador: Diego Sebastian Ledesma<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T22:36:25Z (GMT). No. of bitstreams: 1 Paula_PedroManfrimMagalhaesde_M.pdf: 1130226 bytes, checksum: bbd8d375ddf7846ed2eafe024103e682 (MD5) Previous issue date: 2015<br>Resumo: Este trabalho apresenta um estudo sobre variedades Riemannianas que possuem um tensor de Bakry-Émery-Ricci com limitações. Inicialmente abordamos tanto aspectos da geometria Riemanniana tradicional como métricas e geodésicas, quanto aspectos mais avançados como as fórmulas de Bochner, Weitzenböck e o teorema de Hodge. Em seguida discutimos a convergência de Gromov-Hausdorff e suas propriedades, além de serem apresentados alguns teoremas como os de Kasue e Fukaya. Por fim estudamos as propriedades topológicas e geométricas de variedades com limitação no tensor de Bakry-Émery-Ricci e o comportamento de tais limitações com respeito à submersões e à convergência de Gromov-Hausdorff<br>Abstract: This work presents a study about Riemannian manifolds having a Bakry-Émery-Ricci tensor with bounds. Initially we approached both the traditional aspects of Riemannian geometry like metrics and geodesics, as more advanced aspects like the Bochner, Weitzenböck formulas and the Hodge's theorem. Then we discussed the Gromov-Hausdorff convergence and its properties, in addition to showing some theorems as those from Kasue and Fukaya. Lastly we studied the topological and geometric properties of manifolds with bounds on the Bakry-Émery-Ricci tensor and the behavior of these bounds with respect to submersions and the Gromov-Hausdorff convergence<br>Mestrado<br>Matematica<br>Mestre em Matemática
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Takei, Yoshitsugu. "THE GEOMETRY OF BICHARACTERISTICS AND THE GLOBAL EXISTENCE OF HOLOMORPHIC SOLUTIONS OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS." 京都大学 (Kyoto University), 1989. http://hdl.handle.net/2433/86416.

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Enders, Joerg. "Generalizations of the reduced distance in the Ricci flow - monotonicity and applications." Diss., Connect to online resource - MSU authorized users, 2008.

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Mazzoni, Michele. "A fibre bundle approach to U(1) symmetries in physics." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16776/.

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In questa tesi si utilizza il formalismo dei fibrati principali per descrivere le propriet`a topologiche globali di sistemi fisici classici e quantistici che presentano simmetrie legate all’azione del gruppo U(1). Nel primo capitolo `e contenuta una esposizione della teoria matematica dei fibrati, con un particolare riguardo ai fibrati principali ed alle strutture differenziali definibili su di essi (forme differenziali di connessione e curvatura). Nel secondo capitolo si impiega il formalismo precedentemente sviluppato per trattare le propriet`a del monopolo magnetico di Dirac e si ottiene una quantizzazione della carica magnetica sulla base di considerazioni di natura topologica. Inoltre, si mostra l’impiego dei fibrati principali U(1) nella costruzione di una descrizione Lagrangiana globale per sistemi quali una particella carica nel campo del monopolo e una particella classica con spin in campo magnetico. Nel terzo capitolo, si descrive teoricamente la comparsa di una fase geometrica (fase di Berry) in sistemi quantistici che evolvono adiabaticamente nel tempo, e si fornisce un’interpretazione geometrica di tale fase come olonomia in un fibrato principale U(1). Il moto di una particella quantistica con spin in campo magnetico quasi-statico e l’effetto Aharonov-Bohm vengono presentati come esempi tipici di manifestazione di una fase geometrica.
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Vallet, Bruno. "Bases de fonctions sur les variétés." Phd thesis, Institut National Polytechnique de Lorraine - INPL, 2008. http://tel.archives-ouvertes.fr/tel-00311743.

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Les bases de fonctions sont des outils indispensables de la géométrie numérique puisqu'ils permettent de représenter des fonctions comme des vecteurs, c'est à dire d'appliquer les outils de l'algèbre linéaire à l'analyse fonctionnelle. Dans cette thèse, nous présentons plusieurs constructions de bases de fonctions sur des surfaces pour la géométrie numérique. Nous commençons par présenter les bases de fonctions usuelles des éléments finis et du calcul extérieur discret, leur théorie et leurs limites. Nous étudions ensuite le Laplacien et sa discrétisation, ce qui nous permettra de construire une base de fonctions particulière: les fonctions propres de l'opérateur de Laplace-Beltrami, ou harmoniques variétés. Celles-ci permettent de généraliser la transformée de Fourier et le filtrage spectral aux fonctions définies sur des surfaces. Nous présentons ensuite des applications de cette base de fonction à la géométrie numérique. En particulier, nous montrons qu'une fois calculée, cette base de fonction permet de filtrer la géométrie en temps interactif. Pour pouvoir définir des bases de fonctions de façon plus indépendante du maillage de la surface, nous nous intéressons ensuite aux paramétrisations globales, et en particulier aux champs de directions à symétries qui permettent de les définir. Ainsi, dans la dernière partie, nous étudions ces champs de directions à symétries, et en particulier leur géométrie et leur topologie. Nous proposons enfin des outils pour les construire, les manipuler et les visualiser.
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Rezende, Alex Carlucci. "A geometria de algumas famílias tridimensionais de sistemas diferenciais quadráticos no plano." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-25112014-142038/.

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Sistemas diferenciais quadráticos planares estão presentes em muitas áreas da matemática aplicada. Embora mais de mil artigos tenham sido publicados sobre os sistemas quadráticos ainda resta muito a se conhecer sobre esses sistemas. Problemas clássicos, e em particular o XVI problema de Hilbert, estão ainda em aberto para essa família. Um dos objetivos dos pesquisadores contemporâneos é obter a classificação topológica completa dos sistemas quadráticos. Devido ao grande número de parâmetros (essa família possui doze parâmetros e, aplicando transformações afins e reescala do tempo, reduzimos esse número a cinco, sendo ainda um número grande para se trabalhar) usualmente subclasses são consideradas nas investigações realizadas. Quando características específicas são levadas em consideração, o número de parâmetros é reduzido e o estudo se torna possível. Nesta tese estudamos principalmente duas subfamílias de sistemas quadráticos: a primeira possuindo um nó triplo semielemental e a segunda possuindo uma selanó semi elemental finita e uma selanó semielemental infinita formada pela colisão de uma sela infinita com um nó infinito. Os diagramas de bifurcação para ambas as famílias são tridimensionais. A família tendo um nó triplo gera 28 retratos de fase topologicamente distintos, enquanto o fecho da família tendo as selasnós dentro do espaço de bifurcação de sua forma normal gera 417. Polinômios invariantes são usados para construir os conjuntos de bifurcação e os retratos de fase topologicamente distintos são representados no disco de Poincaré. Os conjuntos de bifurcação são a união de superfícies algébricas e superfícies cuja presença foi detectada numericamente. Ainda nesta tese, apresentamos todos os retratos de fase de um sistema diferencial conhecido como modelo do tipo SIS (sistema suscetívelinfectadosuscetível, muito comum na matemática aplicada) e a classificação dos sistemas quadráticos possuindo hipérboles invariantes. Ambos sistemas foram investigados usando de polinômios invariantes afins.<br>Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilberts 16th problem, are still open for this family. One of the goals of recent researchers is the topological classification of quadratic systems. As this attempt is not possible in the whole class due to the large number of parameters (twelve, but, after affine transformations and time rescaling, we arrive at families with five parameters, which is still a large number), many subclasses are considered and studied. Specific characteristics are taken into account and this implies a decrease in the number of parameters, which makes possible the study. In this thesis we mainly study two subfamilies of quadratic systems: the first one possessing a finite semielemental triple node and the second one possessing a finite semielemental saddlenode and an infinite semielemental saddlenode formed by the collision of an infinite saddle with an infinite node. The bifurcation diagram for both families are tridimensional. The family having the triple node yields 28 topologically distinct phase portraits, whereas the closure of the family having the saddlenodes within the bifurcation space of its normal form yields 417. Invariant polynomials are used to construct the bifurcation sets and the phase portraits are represented on the Poincaré disk. The bifurcation sets are the union of algebraic surfaces and surfaces whose presence was detected numerically. Moreover, we also present the analysis of a differential system known as SIS model (this kind of systems are easily found in applied mathematics) and the complete classification of quadratic systems possessing invariant hyperbolas.
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Rossi, Salvemini Clara. "Espace-temps globalement hyperboliques conformément plats." Phd thesis, Université d'Avignon, 2012. http://tel.archives-ouvertes.fr/tel-00934781.

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Les espace-temps conformément plats de dimension supérieure ou égal à 3 sont des variétés localement modelées l'espace-temps d'Einstein où il agit la composante connexe de l'identité du groupe des difféomorfismes conformes.Un espace-temps M est globalement hyperbolique s'il admet une hypersurface S de type espace qui est rencontrée une et une seule fois par toute courbe causale de M. L'hypersurface S est alors dite hypersurface de Cauchy de M.L'ensemble des espace-temps globalement hyperboliques conformément plats, identifiés à difféomorphisme conforme près, est naturellement muni d'une relation d'ordre partielle: on dit que N étends M s'il existe un plongement conforme de M dans N tel que l'image de toute hypersurface de Cauchy de M est une hypersurface de Cauchy de N. Les éléments maximaux par rapport à cette relation d'ordre sont appelés espace-temps maximaux.Le premier résultat qu'on a prouvé est l'existence et unicité de l'extension maximale pour un espace-temps conformément plat globalement hyperbolique donné. Ce résultat généralise un théorème de Choquet-Bruhat et Geroch relatif aux espace-temps solutions des équation d'Einstein.L'unicité de l'extension maximale permet de prouver le résultat suivant:Théorème:En dimension supérieur ou égal à 3, l'espace d'Einstein est le seul espace-temps conformément plat maximal simplement connexe admettant une hypersurface de Cauchy compacte.Si l'hypersurface de Cauchy S du revêtement universel d'un espace-temps M est compacte on obtient donc que M est un quotient fini de l'espace d'Einstein. La structure des géodésiques de l'espace d'Einstein et l'unicité de l'extension maximale permettent de prouver :Théorème:Soit M un espace-temps conformément plat maximal de dimension supérieur ou égal à 3, qui contient deux géodésiques lumières distinctes, librement homotopes et ayant les mêmes extrémités. Alors M est un quotient fini de l'espace d'Einstein.Dans le cas où l'hypersurface S' du revêtement universel M' de M est non compacte on montre chaque point p de M' est déterminé par le compact de S 'constitué par l'intersection de son passé causal ou de son futur causal avec l'hypersurface S', suivant que p appartient au passé ou au futur de S'. Onappelle ce compact l'ombre de p sur S'. L'espace-temps M' s'identifie donc à un sous-ensemble des compacts de S'.Ce point de vue permet d'avoir une compréhension plus profonde de la maximalité d'un espace-temps. En fait on a différentes notions de maximalité :un espace-temps pourrait être maximal parmi les espace-temps conformément plats mais avoir un majorant qui n'est pas conformément plat, i.e. il pourrait exister un plongement conforme dans un espace-temps globalement hyperbolique qui ne soit pas conformément plat.Grâce à la notion d'ombre, on prouve que la structure causale induite sur la frontière de Penrose du revêtement universel d'un espace-temps conformément plat permet de caractériser les espace-temps maximaux parmi tous les espace-temps globalement hyperboliques, on obtient:Théorème:Tout espace-temps globalement hyperbolique conformément plat M qui est maximal parmi les espace-temps globalement hyperbolique conformément plats est aussi maximal parmi tous les espace-temps globalement hyperboliques.On conclut avec une discussion détaillée sur la maximalité des espaces-temps globalement hyperboliques maximaux parmi les espace-temps à courbure constante, suivant le signe de la courbure: lorsque la courbure est négative ou nulle, l'espace-temps est maximal aussi parmi tous les espace-temps globalement hyperboliques, mais cela n'est jamais vrai lorsque la courbure est strictement positive
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Books on the topic "Differential geometry – Global differential geometry – Global differential geometry"

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Bär, Christian, Joachim Lohkamp, and Matthias Schwarz, eds. Global Differential Geometry. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-22842-1.

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Joachim, Lohkamp, Schwarz Matthias, and SpringerLink (Online service), eds. Global Differential Geometry. Springer-Verlag Berlin Heidelberg, 2012.

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Cordero, Luis A. Differential Geometry of Frame Bundles. Springer Netherlands, 1988.

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Ferus, Dirk, Ulrich Pinkall, Udo Simon, and Berd Wegner, eds. Global Differential Geometry and Global Analysis. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0083621.

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Beem, John K. Global Lorentzian geometry. 2nd ed. Marcel Dekker, 1996.

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Parrott, Stephen. Relativistic Electrodynamics and Differential Geometry. Springer New York, 1987.

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Global calculus. American Mathematical Society, 2005.

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Ramanan, S. Global calculus. American Mathematical Society, 2005.

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Ferus, Dirk, Robert B. Gardner, Sigurdur Helgason, and Udo Simon, eds. Global Differential Geometry and Global Analysis 1984. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0075080.

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1938-, Simon Udo, and Zhao Guosong 1950-, eds. Global affine differential geometry of hypersurfaces. De Gruyter, 1993.

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Book chapters on the topic "Differential geometry – Global differential geometry – Global differential geometry"

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Hitchin, Nigel. "Global Differential Geometry." In Mathematics Unlimited — 2001 and Beyond. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56478-9_29.

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Freyn, Walter. "Kac-Moody Geometry." In Global Differential Geometry. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22842-1_3.

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Bernig, Andreas. "Algebraic Integral Geometry." In Global Differential Geometry. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22842-1_5.

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Pressley, Andrew. "Global properties of curves." In Elementary Differential Geometry. Springer London, 2010. http://dx.doi.org/10.1007/978-1-84882-891-9_3.

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Pressley, Andrew. "Global Properties of Curves." In Elementary Differential Geometry. Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-3696-5_3.

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Schwachhöfer, Lorenz J. "Holonomy Groups and Algebras." In Global Differential Geometry. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22842-1_1.

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Hanke, Bernhard. "Positive Scalar Curvature, K-area and Essentialness." In Global Differential Geometry. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22842-1_10.

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Bunke, Ulrich, and Thomas Schick. "Differential K-Theory: A Survey." In Global Differential Geometry. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22842-1_11.

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Bär, Christian, and Nicolas Ginoux. "Classical and Quantum Fields on Lorentzian Manifolds." In Global Differential Geometry. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22842-1_12.

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Goette, Sebastian. "Computations and Applications of η Invariants." In Global Differential Geometry. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22842-1_13.

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Conference papers on the topic "Differential geometry – Global differential geometry – Global differential geometry"

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Richter, Thomas. "SSIM as global quality metric: A differential geometry view." In 2011 Third International Workshop on Quality of Multimedia Experience (QoMEX 2011). IEEE, 2011. http://dx.doi.org/10.1109/qomex.2011.6065701.

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Richter, Thomas. "From index to metric: using differential geometry to define a global visual quality metric." In SPIE Optical Engineering + Applications, edited by Andrew G. Tescher. SPIE, 2011. http://dx.doi.org/10.1117/12.896091.

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Ma, Baoshun, Robert Harbaugh, Jia Lu, and Madhavan Raghavan. "Modeling the Geometry, Hemodynamics and Tissue Mechanics of Cerebral Aneurysms." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60024.

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The relationship between cerebral aneurysm geometry and biomechanics was investigated. Human cerebral aneurysm geometry was reconstructed from computed tomography angiography (CTA) and refined. Various indices of global geometric (size and shape) features were computed based on differential and computational geometry techniques. Computational fluid dynamics (CFD) simulations were performed to model both steady and pulsatile blood flow in the aneurysm and surrounding vasculature. Hemodynamic indices such as wall shear stress, pressure and particle residence time were obtained. Nonlinear finite element method (FEM) and a reported finite strain constitutive model were employed to estimate the distribution of mechanical stress in the aneurysm wall under static pressure. Shear stress, sac pressure and mechanical stress correlated better with lesion shape while particle residence time correlated better with lesion size.
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O̸stergaard, Niels H., Anders Lyckegaard, and Jens H. Andreasen. "On Lateral Buckling Failure of Armour Wires in Flexible Pipes." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-49358.

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This paper introduces the concept of lateral buckling of tensile armour wires in flexible pipes as a failure mode. This phenomenon is governed by large deflections and is therefore highly non-linear. A model for prediction of the wire equilibrium state within the pipe wall based on force equilibrium in curved beams and curvature expressions derived from differential geometry is presented. On this basis, a model of the global equilibrium state of the armour layers in flexible pipes is proposed. Furthermore, it is demonstrated how this model can be used for lateral buckling prediction. Obtained results are compared with experiments.
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Ghaderi, P., and M. Bankehsaz. "Effects of Material Properties Estimations on the Thermo-Elastic Analysis for Functionally Graded Thick Spheres and Cylinders." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41475.

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In this paper effects of material properties estimations, used for particulate reinforced composites, on the thermo-mechanical response of functionally graded sphere and cylinder are presented. A numerical solution for an arbitrary material gradation is obtained for each geometry independently. With this assumption, the governing partial differential equations are reduced to an ordinary differential equation in each geometry. The thermo-elastic solution for hollow sphere is derived using spherical symmetry. However, plane strain and axial symmetry are assumed for solving hollow cylinder. In the numerical method, radial domain is divided into some finite sub-domains and material properties are assumed to be constant in each sub-domain. With this assumption, the governing thermal and mechanical equations in each sub-domain are an ODE with constant coefficients. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the thermo-elastic responses for the thick-walled FG sphere and cylinder are obtained. Three methods of gradation are used for comparing the effects of different material properties estimations on the results; Rule of Mixtures as a conventional method, Mori-Tanaka estimation and self-consistent scheme. The results show that estimations for material properties could be influential to the thermo-elastic response for some profiles of volume fractions of constituents. However, the effect on elastic response is negligible.
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Müller, Andreas. "A Screw Approach to the Approximation of the Local Geometry of the Configuration Space and of the Set of Configurations of Certain Rank of Lower Pair Linkages." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85526.

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The determination of the finite mobility of a linkage boils down to the analysis of its configuration space (c-space). Since a global analysis is not feasible in general (but only for particular cases), the research focused on methods for a local analysis. Past research has in particular addressed the approximation of finite curves in c-space (i.e. finite motions). No universal method for the approximation of the c-space itself has been reported. In this paper a generally applicable formulation of the equations defining the higher-order local approximation of the c-space as well as the set of points where the Jacobian has a certain rank are presented. To this end, algebraic formulations of the higher-order differential of the constraint mapping (defining the loop closure) and of the Jacobian minors of arbitrary order are introduced. The respective local approximation is therewith given in terms of a low-order polynomial system. Results are shown for a simple planar 4-bar linkage and a planar three-loop linkage. Since the latter exhibits a cusp singularity it cannot be treated by the local analysis methods proposed thus far, which are based on approximating finite curves.
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Chen, Li Hua, Shou Jie Cui, Xiao Zhi Zhang, and Wei Zhang. "Study on Large Deformation of Laminated Piezoelectric Rectangular Plate." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-88599.

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For the laminated piezoelectric rectangular plate with large deflection and large rotation, the nonlinear equilibrium differential equations are derived and solved. Firstly, the global Cartesian coordinate system to describe the undeformed geometry and the local orthogonal curvilinear coordinate system to describe the deformed geometry are established respectively on the mid-plane of the plate before and after the deformation, and the relationship between the two coordinates is expressed by transformation matrix. For the convenience of calculation, the expressions of the nonlinear curvatures and inplane strains are obtained by Taylor series expansion. Considering the piezoelectric effect, three equilibrium partial differential equations describing nonlinear bending problems are obtained by the principle of virtual work. Furthermore, in order to simplify the solution process, the stress function is introduced to automatically satisfy the first two equations for the large deformation of the cantilever plate, and the relationship between stress function, the mid-plane internal force and shear force is also given for the first time. Therefore, the stress function and the transversal displacement are the main unknowns of the governing equation and compatibility equation. Additionally, the approximate deflection function and stress function are given which can satisfy all the displacement boundary conditions and only part of the force boundary conditions. Thereby, the generalized Galerkin method is used to obtain the approximate solution of the nonlinear bending problem. Finally, the results in the study are verified by comparison with the results obtained from the finite element method. It also provides a theoretical basis for the engineering application of the large deformation of the piezoelectric cantilever plate.
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Karam, A., and D. Play. "A Discrete Analysis of Metal-V Belt Drive." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0040.

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Abstract The metal-V belt drive includes a large number of parts which interact between them to transmit power from the input to the output pulleys. A compression belt composed of a great number of struts is maintained by a tension flat belt. Power is them shared into the two belts that moves generally in opposite directions. Due to the particular geometry of the elements and to the great number of parts, a numerical approach achieves the global equilibrium of the mechanism from the elementary part equilibrium. Sliding arc on each pulley can be thus defined both for the compression and tension belts. Finally, power sharing can be calculated as differential motion between the belts, is defined. The first part of the paper will present the different steps of the quasi-static mechanical analysis and their numerical implementations. Load distributions, speed profiles and sliding angle values will be discussed. The second part of the paper will deal to a systematic use of the computer software. Speed ratio, transmitted torque, strut geometry and friction coefficients effect will be analysed in relation with the output parameter variations. Finally, the effect pulley deformable flanges will be discussed.
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Sbutega, Krsto, and Ivan Catton. "Application of Fourier-Galerkin Method to Volume Averaging Theory Based Model of Heat Sinks." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65244.

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Efficient analysis of heat sink performance is a crucial step in the optimization process of such devices. Accurate analysis of these complex geometric systems with CFD and FE methods requires fine meshes, which imply significant computational time. In this study, Volume Averaging Theory (VAT) is rigorously applied to obtain a geometrically simplified but physically accurate model for any periodic heat sink geometry. The governing equations are averaged over a Representative Averaging Volume (REV) to obtain a set of integro-differential equations. Some information about lower level phenomena is lost in every averaging process and a closure scheme is required to model these behaviors. Experimental data for friction factor and Nusselt number in an REV is used to close the set of PDEs. This mathematical process replaces the complex geometry of the heat sink with a fictitious continuous medium and smoothens the quantities of interest throughout the system. These system features allow the use of a global Fourier-Galerkin method to efficiently solve the resulting equations and accurately predict the performance of the system. The effectiveness of the method is proven by applying it to model thermal behavior for laminar flow over an air-cooled pin-fin heat sink and a water-cooled micro-channel heat sink. The convergence in the Nusselt number in the case of constant heat flux is found to be quadratic with respect to the number of basis functions. The accuracy of the method is validated by comparing the numerical results obtained to existing experimental data. The maximum difference between the predicted Nusselt number and the experimental measurements is found to be only 4% for both cases.
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Bakshi, Soham, Badih A. Jawad, Selin Arslan, Kingman Yee, and Liping Liu. "Multi-Objective Optimization of a Simplified Car Body Using Computational Fluid Dynamics." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52913.

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Today’s strict fuel economy requirement produces the need for the cars to have really optimized shapes among other characteristics as optimized cooling packages, reduced weight, to name a few. With the advances in automotive technology, tight global oil resources, lightweight automotive design process becomes a problem deserving important consideration. It is not however always clear how to modify the shape of the exterior of a car in order to minimize its aerodynamic resistance. Air motion is complex and operates differently at different weather conditions. This gap can be covered by the use of adjoint solvers which predict the sensibility of the aerodynamic forces to changes of the geometry. Alternatively, Computational Fluid Dynamics (CFD) solvers can be partnered with optimization software which guide model design changes and evaluate the corresponding results. Design changes can be executed by modifying a parameterized geometry or using mesh morphing techniques. With the advances in computational fluid dynamics, design optimization methods in the aerodynamic design are more important than ever. In the present paper, ANSYS Fluent will be used in conjunction with the optimization software ANSYS DesignXplorer to study ways of reducing drag and lift for a simplified car body. ANSYS simulation software allows one to predict, with confidence, the impact of fluid flows on the product throughout design and manufacturing as well as during end use. CFD is a complex technology involving strongly coupled non-linear partial differential equations which attempt to computationally simulate theoretical and experimental models in a discrete domain of complex geometric shape. A detailed assessment of errors and uncertainties has to concern itself with the three roots of CFD: theory, experiment, and computation. Further, the application of CFD is rapidly expanding with the growth in computational resources. The body in question in this study is the Ahmed body [1] which has been used numerous times for CFD code validation. This geometry represents a road legal car which is used to study the effect of different forces like, aerodynamic drag force, lift force, and some other major forces which affect a car’s motion significantly. Despite being a simple body, accurate prediction of its aerodynamic performance often requires very accurate and computationally expensive calculations. We would like to investigate if meaningful optimizations can be achieved by using reduced resources, by analyzing how air at different velocity affect the body and what changes might be necessary for a further optimized performance. The purpose here is not to predict the absolute values of drag for this body, but to demonstrate that optimization can be performed with limited resources relying on information about drag deltas rather than absolute values. Keeping limiting resources in mind, a grid independence study wasn’t done.
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