Relevant bibliographies by topics / Tangent bundles

Contents

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

Academic literature on the topic 'Tangent bundles'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 July 2024

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Journal articles on the topic "Tangent bundles"

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Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman and Makarim Abdullah Mohammed Ali Mohammed. "Investigate A New Tangent Bundle Space from A New Point and Two Curves using MATLAB." IJRDO -JOURNAL OF MATHEMATICS 10, no. 1 (January 25, 2024): 1–11. http://dx.doi.org/10.53555/m.v10i1.5979.

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Our goal was to create a new tangent bundle space from a new point and two curves using the MATLAB program. We used the applied mathematical approach, and we arrived at an accurate model of the tangent bundle space by building an algorithm that implements the solution and displays the results and represents them graphically with ease and with high accuracy. This is what MATLAB makes a suitable working environment for dealing with tangent bundles. Given the importance of tangent bundles in modern engineering and physical sciences, this algorithm can be developed to include the most important areas of tangent bundles instead of the complex traditional method
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ISIDRO, JOSÉ M. "QUANTUM STATES FROM TANGENT VECTORS." Modern Physics Letters A 19, no. 31 (October 10, 2004): 2339–52. http://dx.doi.org/10.1142/s0217732304015634.

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We argue that tangent vectors to classical phase space give rise to quantum states of the corresponding quantum mechanics. This is established for the case of complex, finite-dimensional, compact, classical phase spaces [Formula: see text], by explicitly constructing Hilbert-space vector bundles over [Formula: see text]. We find that these vector bundles split as the direct sum of two holomorphic vector bundles: the holomorphic tangent bundle [Formula: see text], plus a complex line bundle [Formula: see text]. Quantum states (except the vacuum) appear as tangent vectors to [Formula: see text]. The vacuum state appears as the fibrewise generator of [Formula: see text]. Holomorphic line bundles [Formula: see text] are classified by the elements of [Formula: see text], the Picard group of [Formula: see text]. In this way [Formula: see text] appears as the parameter space for nonequivalent vacua. Our analysis is modelled on, but not limited to, the case when [Formula: see text] is complex projective space CPn.
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Sultanov, A. Ya, G. A. Sultanova, and N. V. Sadovnikov. "Affine transformations of the tangent bundle with a complete lift connection over a manifold with a linear connection of special type." Differential Geometry of Manifolds of Figures, no. 52 (2021): 137–43. http://dx.doi.org/10.5922/0321-4796-2021-52-13.

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The theory of tangent bundles over a differentiable manifold M be­longs to the geometry and topology of manifolds and is an intensively developing area of the theory of fiber spaces. The foundations of the theo­ry of fibered spaces were laid in the works of S. Eresman, A. Weil, A. Mo­ri­moto, S. Sasaki, K. Yano, S. Ishihara. Among Russian scientists, tangent bund­les were investigated by A. P. Shirokov, V. V. Vishnevsky, V. V. Shu­rygin, B. N. Shapukov and their students. In the study of automorphisms of generalized spaces, the question of infinitesimal transformations of connections in these spaces is of great importance. K. Yano, G. Vrancianu, P. A. Shirokov, I. P. Egorov, A. Z. Pet­rov, A. V. Aminova and others have studied movements in different spac­es. The works of K. Sato and S. Tanno are devoted to the motions and au­tomorphisms of tangent bundles. Infinitesimal affine collineations in tan­gent bundles with a synectic connection were considered by H. Shadyev. At present, the question of the motions of fibered spaces is considered in the works of A. Ya. Sultanov, in which infinitesimal transformations of a bundle of linear frames with a complete lift connection, the Lie algebra of holomorphic affine vector fields in arbitrary Weyl bundles are investi­gated. In this paper we obtain exact upper bounds for the dimensions of Lie algebras of infinitesimal affine transformations in tangent bundles with a synectic connection A. P. Shyrokov.
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Sultanov, A. Ya, and G. A. Sultanova. "On the local representation of synectic connections on Weil bundles." Differential Geometry of Manifolds of Figures, no. 53 (2022): 118–26. http://dx.doi.org/10.5922/0321-4796-2022-53-11.

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Synectic extensions of complete lifts of linear connections in tangent bundles were introduced by A. P. Shirokov in the seventies of the last century [1; 2]. He established that these connections are linear and are real realizations of linear connections on first-order tangent bundles en­do­wed with a smooth structure over the algebra of dual numbers. He also pro­ved the existence of a smooth structure on tangent bundles of arbitrary or­der on a smooth manifold M over the algebra of plu­ral numbers. Studying holomorphic linear connections on over an algebra , A. P. Shirokov obtained real realizations of these con­nec­tions, which he called Synectic extensions of a linear connection defi­ned on M. A natural generalization of the algebra of plural numbers is the A. Weyl algebra, and a generalization of the tangent bundle is the A. Weyl bundle. It was shown in [3] that a synectic extension of linear connections defined on M a smooth manifold can also be constructed on A. Weyl bundles , where is the A. Weyl algebra. The geometry of these bundles has been studied by many authors — A. Morimoto, V. V. Shu­rygin and others. A detailed analysis of these works can be found in [3]. In this paper, we study synectic lifts of linear connections defined on A. Weyl bundles.
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Jacobowitz, Howard, and Gerardo Mendoza. "Sub-bundles of the complexified tangent bundle." Transactions of the American Mathematical Society 355, no. 10 (June 10, 2003): 4201–22. http://dx.doi.org/10.1090/s0002-9947-03-03350-6.

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Feizabadi, Hassan, and Naser Boroojerdian. "Extending Tangent Bundles by an Algebra Bundle." Iranian Journal of Science and Technology, Transactions A: Science 42, no. 2 (February 13, 2018): 615–21. http://dx.doi.org/10.1007/s40995-018-0515-y.

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Ali, Sahadat. "Prolongation of Tensor Fields and G-Structures in Tangent Bundles of Second Order." Journal of the Tensor Society 9, no. 01 (June 30, 2009): 77–81. http://dx.doi.org/10.56424/jts.v9i01.10563.

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Tangent and cotangent bundles have been defined and studied by Yano, Ishihara, Patterson and others. Duggal gives the notion of GF-structure, which plays an important role in the differentiable manifold [1]. R. Nivas and Ali have studied the existence of GF-structure and generalized contact structure on the tangent bundle and some interesting results have been obtained for such structures [2]. Prolongation of tensor fields, almost complex and almost product structures have been defined and studied by Yano, Ishihara [3] and others whereas Das [4] and Morimoto [5] have studied the prolongation of F-structure and G-structures respectively to the tangent bundles. In the present paper problems of prolongation in tangent bundle of second order and few results on GF, fa(3, −1) and generalized contact structures have been discussed.
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Li, Tongzhu, and Demeter Krupka. "The Geometry of Tangent Bundles: Canonical Vector Fields." Geometry 2013 (April 14, 2013): 1–10. http://dx.doi.org/10.1155/2013/364301.

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A canonical vector field on the tangent bundle is a vector field defined by an invariant coordinate construction. In this paper, a complete classification of canonical vector fields on tangent bundles, depending on vector fields defined on their bases, is obtained. It is shown that every canonical vector field is a linear combination with constant coefficients of three vector fields: the variational vector field (canonical lift), the Liouville vector field, and the vertical lift of a vector field on the base of the tangent bundle.
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CRASMAREANU, MIRCEA. "DIRAC STRUCTURES FROM LIE INTEGRABILITY." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1220005. http://dx.doi.org/10.1142/s0219887812200058.

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We prove that a pair (F = vector sub-bundle of TM, its annihilator) yields an almost Dirac structure which is Dirac if and only if F is Lie integrable. Then a flat Ehresmann connection on a fiber bundle ξ yields two complementary, but not orthogonally, Dirac structures on the total space M of ξ. These Dirac structures are also Lagrangian sub-bundles with respect to the natural almost symplectic structure of the big tangent bundle of M. The tangent bundle in Riemannian geometry is discussed as particular case and the 3-dimensional Heisenberg space is illustrated as example. More generally, we study the Bianchi–Cartan–Vranceanu metrics and their Hopf bundles.
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Abbassi, Mohamed Tahar Kadaoui, and Ibrahim Lakrini. "On the completeness of total spaces of horizontally conformal submersions." Communications in Mathematics 29, no. 3 (December 1, 2021): 493–504. http://dx.doi.org/10.2478/cm-2021-0031.

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Abstract In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.
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Dissertations / Theses on the topic "Tangent bundles"

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Tureli, Sina. "Integrability of Continuous Tangent Sub-bundles." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4876.

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In this thesis, the main aim is to study the integrability properties of continuous tangent sub-bundles, especially those that arise in the study of dynamical systems. After the introduction and examples part we start by studying integrability of such sub-bundles under different regularity and dynamical assumptions. Then we formulate a continuous version of the classical Frobenius theorem and state some applications to such bundles, to ODE and PDE. Finally we close of by stating some ongoing work related to interactions between integrability, sub-Riemannian geometry and contact geometry.
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Hindeleh, Firas. "Tangent and cotangent bundles automorphism groups and representations of Lie groups /." See Full Text at OhioLINK ETD Center (Requires Adobe Acrobat Reader for viewing), 2006. http://www.ohiolink.edu/etd/view.cgi?acc_num=toledo1153933389.

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Thesis (Ph.D.)--University of Toledo, 2006.
Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 79-82.
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Hindeleh, Firas Y. "Tangent and Cotangent Bundles, Automorphism Groups and Representations of Lie Groups." University of Toledo / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1153933389.

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Wang, Hongyuan. "On a class of algebraic surfaces with numerically effective cotangent bundles." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1154450131.

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Pavolaitė, Miglė. "Simetrinės trečiosios eilės liestinės sluoksniuotės." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100709_091446-82031.

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Darbe nagrinėjamos simetrinės trečiosios eilės liestinės sluoksniuotės, kurios apibrėžiamos kaip 3 - džetų aibės. Surasta simetrinės erdvės izotropijų grupė, o taip pat jos izomorfijų grupė. Gautos izomorfijų grupės struktūrinės lygtys, surasti erdvės Maurerio – Kartano lygčių analogai, įrodytos formulės, išreiškiančios indukuotosios afiniosios sieties kreivumo tenzorių komponentes izomorfijų grupės struktūrinėmis konstantomis. Taip pat gauta visa eilė tapatybių, siejančių kreivumo objektus ir izomorfijų grupės struktūrines konstantas (apibendrintos Ričio ir Bianchi tapatybės).
The paper examined the symmetric third order tangent bundle, defined as 3- jet space. Found symmetric space isotropy group, as well as its isomorphy group. The resulting structural equation of isomorphy group, find this area Maurer - Cartan analogues of equations, an established formula, expressing inducted affines connection component of curvature tensors of the isomorphy group structural constants. Also received identities connecting the curvature objects structural constants of isomorphy group (generalized in Riči and Bianchi identity).
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Mickutė, Laura. "Apie trečios eilės liestinių sluoksniuočių geometriją." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050623_101559-72938.

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In this work is analysed the tangent bundle geometry order 3. Those bundles are defined like 3 - jet space. Co - ordinates transformation formulas of those bundles are received, how the object of linear connection inducted affine connections is demonstrated. In this work the theorem how the object of linear connection of tangent bundle inducted linear connection of tangent bundle order 3 is proved.
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Silva, Rafael Barbosa da. "Existência de conexões versus módulos projetivos." Universidade Federal da Paraí­ba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7424.

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Made available in DSpace on 2015-05-15T11:46:16Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 578974 bytes, checksum: e512f47deae8cd03667ae8e7c2143b34 (MD5) Previous issue date: 2013-05-03
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The notions of connection and covariant derivative has its origin in the field of Riemannian geometry , where there is no distinction between them. In fact, in this study we found that these notions are equivalent if we consider modules over K-algebras of finite type. We also show that the existence of connections implies the existence of covariant derivative. The main goal of this study is to determine which modules admit connections. We easily verified that the projective modules admit connections. In fact, they form an affine space. But we also display a module that is not projective and has connection. Later, inspired by Swan's theorem, we explore in a straightforward way modules formed by sections of the tangent bundle of some surfaces in 3-dimensional real space. Finally, we study the notion of connection introduced by Alain Connes in modules over K-algebras not necessarily commutative. And we find in that context that the modules that have connection are exactly the projectives modules.
As noções de conexão e derivada covariante tem sua origem na área de geometria riemanniana, onde não existe distinção entre elas. De fato, nós verificamos neste trabalho, que estas noções são equivalentes se considerarmos módulos sobre K-álgebras comutativas de tipo finito. Também mostramos que a existência de conexões implica na existência de derivada covariante. O objetivo central deste trabalho é determinar que módulos admitem conexão. Verificamos facilmente que os módulos projetivos admitem conexões. De fato, elas formam um espaço afim. Mas também exibimos um módulo não projetivo que possui conexão. Posteriormente, inspirados pelo teorema de Swan, exploramos de maneira direta os módulos formados pelas seções do fibrado tangente de algumas superfícies no espaço 3- dimensional real. Por fim, estudamos a noção de conexão introduzida por Alain Connes em módulos sobre K-álgebras não necessariamente comutativas. E verificamos nesse contexto que os módulo que admitem conexão são exatamente os módulos projetivos.
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Kravčenkaitė, Deimantė. "Euklido erdvės liečiamojo pluošto hiperpaviršių struktūra ir geometrinė prasmė." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20120702_110845-55808.

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Šis darbas pratęsia 2010 m. autorės atlikto bakalauro darbo „Elipsinio tipo B-erdvių beveik kontaktiniai metriniai hiperpaviršiai“ tyrinėjimus, apibendrina šio darbo rezultatus kitų tipų ir rūšių -struktūroms ir pritaiko juos liečiamųjų sluoksniuočių paviršių teorijoje.
In the work, the generalized (φ, ξ, η, g)-structures in normalized hypersurfaces M2n-1 T(En) are found and its properties are investigated. Geometric meaning in basis En of some interesting hypersurfaces (hypersphere, hyperplane, hypercone,…) is explained.
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Simsir, Muazzez Fatma. "Conformal Vector Fields With Respect To The Sasaki Metric Tensor Field." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605857/index.pdf.

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On the tangent bundle of a Riemannian manifold the most natural choice of metric tensor field is the Sasaki metric. This immediately brings up the question of infinitesimal symmetries associated with the inherent geometry of the tangent bundle arising from the Sasaki metric. The elucidation of the form and the classification of the Killing vector fields have already been effected by the Japanese school of Riemannian geometry in the sixties. In this thesis we shall take up the conformal vector fields of the Sasaki metric with the help of relatively advanced techniques.
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Bauer, David. "Towards Discretization by Piecewise Pseudoholomorphic Curves." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-132065.

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This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g). For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation. The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data. For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition.
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Books on the topic "Tangent bundles"

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Kashiwara, Masaki. Introduction to microlocal analysis. Gene ve: L'Enseignement mathe matique, Universite de Gene ve, 1986.

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Arapura, Donu. Threefolds with semipositive tangent bundle. 1985.

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Mann, Peter. Linear Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0037.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree of mathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactly what is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.
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Mann, Peter. Differential Geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0038.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree ofmathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactlywhat is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.
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Mann, Peter. Coordinates & Constraints. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0006.

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This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.
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Mann, Peter. Constrained Hamiltonian Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0021.

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This chapter focuses on autonomous geometrical mechanics, using the language of symplectic geometry. It discusses manifolds (including Kähler manifolds, Riemannian manifolds and Poisson manifolds), tangent bundles, cotangent bundles, vector fields, the Poincaré–Cartan 1-form and Darboux’s theorem. It covers symplectic transforms, the Marsden–Weinstein symplectic quotient, presymplectic and symplectic 2-forms, almost symplectic structures, symplectic leaves and foliation. It also discusses contact structures, musical isomorphisms and Arnold’s theorem, as well as integral invariants, Nambu structures, the Nambu bracket and the Lagrange bracket. It describes Poisson bi-vector fields, Poisson structures, the Lie–Poisson bracket and the Lie–Poisson reduction, as well as Lie algebra, the Lie bracket and Lie algebra homomorphisms. Other topics include Casimir functions, momentum maps, the Euler–Poincaré equation, fibre derivatives and the geodesic equation. The chapter concludes by looking at deformation quantisation of the Poisson algebra, using the Moyal bracket and C*-algebras to develop a quantum physics.
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Mann, Peter. The Hamiltonian & Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0014.

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This chapter discusses the Hamiltonian and phase space. Hamilton’s equations can be derived in several ways; this chapter follows two pathways to arrive at the same result, thus giving insight into the motivation for forming these equations. The importance of deriving the same result in several ways is that it shows that, in physics, there are often several mathematical avenues to go down and that approaching a problem with, say, the calculus of variations can be entirely as valid as using a differential equation approach. The chapter extends the arenas of classical mechanics to include the cotangent bundle momentum phase space in addition to the tangent bundle and configuration manifold, and discusses conjugate momentum. It also introduces the Hamiltonian as the Legendre transform of the Lagrangian and compares it to the Jacobi energy function.
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Mann, Peter. The Jacobi Energy Function. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0010.

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This chapter focuses on the Jacobi energy function, considering how the Lagrange formalism treats the energy of the system. This discussion leads nicely to conservation laws and symmetries, which are the focus of the next chapter. The Jacobi energy function associated with a Lagrangian is defined as a function on the tangent bundle. The chapter also discuss explicit vs implicit time dependence, and shows how time translational invariance ensures the generalised coordinates are inertial, meaning that the energy function is the total energy of the system. In addition, it examines the energy function using non-inertial coordinates and explicit time dependence.
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Mann, Peter. Symmetries & Lagrangian-Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0011.

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This chapter discusses conservation laws in Lagrangian mechanics and shows that certain conservation laws are just particular examples of a more fundamental theory called ‘Noether’s theorem’, after Amalie ‘Emmy’ Noether, who first discovered it in 1918. The chapter starts off by discussing Noether’s theorem and symmetry transformations in Lagrangian mechanics in detail. It then moves on to gauge theory and surface terms in the action before isotropic symmetries. continuous symmetry, conserved quantities, conjugate momentum, cyclic coordinates, Hessian condition and discrete symmetries are discussed. The chapter also covers Lie algebra, spontaneous symmetry breaking, reduction theorems, non-dynamical symmetries and Ostrogradsky momentum. The final section of the chapter details Carathéodory–Hamilton–Jacobi theory in the Lagrangian setting, to derive the Hamilton–Jacobi equation on the tangent bundle!
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Book chapters on the topic "Tangent bundles"

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Blair, David E. "Tangent Bundles and Tangent Sphere Bundles." In Riemannian Geometry of Contact and Symplectic Manifolds, 137–55. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4757-3604-5_9.

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Blair, David E. "Tangent Bundles and Tangent Sphere Bundles." In Riemannian Geometry of Contact and Symplectic Manifolds, 169–93. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4959-3_9.

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Hasegawa, Izumi, and Kazunari Yamauchi. "Infinitesimal Projective Transformations on Tangent Bundles." In Finsler and Lagrange Geometries, 91–98. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0405-2_9.

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Antonelli, P. L., and T. J. Zastawniak. "Diffusion on the Tangent and Indicatrix Bundles." In Fundamentals of Finslerian Diffusion with Applications, 159–74. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4824-5_7.

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Antonelli, P. L. "Diffusion on the Tangent and Indicatrix Bundles." In Handbook of Finsler Geometry, 319–33. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-007-0942-3_16.

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Opozda, Barbara. "On the Tangent Bundles of Statistical Manifolds." In Lecture Notes in Computer Science, 199–206. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38271-0_20.

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Maurin, Krzysztof. "Tangent Bundle TM. Vector, Fiber, Tensor and Tensor Densities, and Associate Bundles." In The Riemann Legacy, 242–52. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8939-0_22.

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Kitayama, Masashi. "Induced Vector Fields in a Hypersurface of Riemannian Tangent Bundles." In Finsler and Lagrange Geometries, 109–11. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0405-2_11.

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Antonelli, P. L., and T. J. Zastawniak. "Diffusion on the Tangent and Indicatrix Bundles of a Finsler Manifold." In The Theory of Finslerian Laplacians and Applications, 89–110. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5282-2_6.

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Peternell, Thomas. "Tangent Bundles, Rational Curves, and the Geometry of Manifolds of Negative Kodaira Dimension." In Complex Analysis and Geometry, 293–310. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4757-9771-8_12.

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Conference papers on the topic "Tangent bundles"

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Kowalski, Oldřich, and Masami Sekizawa. "Invariance of g-natural metrics on tangent bundles." In Proceedings of the 10th International Conference on DGA2007. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790613_0015.

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CHO, JONG TAEK, and SUN HYANG CHUN. "A NEW STRUCTURE ON UNIT TANGENT SPHERE BUNDLES." In Proceedings in Honor of Professor K Sekigawa's 60th Birthday. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701701_0005.

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VACARU, SERGIU I. "COVARIANT RENORMALIZABLE GRAVITY THEORIES ON (NON) COMMUTATIVE TANGENT BUNDLES." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0398.

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KAJIGAYA, Toru. "ON THE MINIMALITY OF NORMAL BUNDLES IN THE TANGENT BUNDLES OVER THE COMPLEX SPACE FORMS." In Proceedings of the International Workshop in Honor of S Maeda's 60th Birthday. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814566285_0022.

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Hasegawa, Izumi, and Kazunari Yamauchi. "Conformally-projectively flat statistical structures on tangent bundles over statistical manifolds." In Proceedings of the 10th International Conference on DGA2007. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790613_0021.

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MANEV, MANCHO. "TANGENT BUNDLES WITH SASAKI METRIC AND ALMOST HYPERCOMPLEX PSEUDO-HERMITIAN STRUCTURE." In Proceedings in Honor of Professor K Sekigawa's 60th Birthday. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701701_0013.

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Leonardos, Spyridon, Xiaowei Zhou, and Kostas Daniilidis. "Articulated motion estimation from a monocular image sequence using spherical tangent bundles." In 2016 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2016. http://dx.doi.org/10.1109/icra.2016.7487183.

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KADAOUI ABBASSI, MOHAMED TAHAR, and OLDŘICH KOWALSKI. "ON G-NATURAL METRICS WITH CONSTANT SCALAR CURVATURE ON UNIT TANGENT SPHERE BUNDLES." In Proceedings in Honor of Professor K Sekigawa's 60th Birthday. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701701_0001.

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Patrick, George W., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Variational Discretizations: Discrete Tangent Bundles, Local Error Analysis, and Arbitrary Order Variational Integrators." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241221.

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SATO, TAKUJI. "ON A FAMILY OF ALMOST KÄHLER STRUCTURES ON THE TANGENT BUNDLES OVER SOME STATISTICAL MODELS." In Proceedings in Honor of Professor K Sekigawa's 60th Birthday. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701701_0017.

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Reports on the topic "Tangent bundles"

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Druta, Simona L. The Sectional Curvature of the Tangent Bundles with General Natural Lifted Metrics. GIQ, 2012. http://dx.doi.org/10.7546/giq-9-2008-198-209.

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Munteanu, Marian Ioan. Old and New Structures on the Tangent Bundle. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-264-278.

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Gezer, Aydin, and Lokman Bilen. Projective Vector Fields on the Tangent Bundle with a Class of Riemannian Metrics. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, May 2018. http://dx.doi.org/10.7546/crabs.2018.05.01.

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Boumaiza, Mohamed. Poisson-Lie Structure on the Tangent Bundle of a Poisson-Lie Group and Poisson Action Lifting. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-4-2005-1-18.

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Zohrehvand, Mosayeb. IFHP Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Pseudo-Riemannian Metrics. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, February 2020. http://dx.doi.org/10.7546/crabs.2020.02.04.

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