Relevant bibliographies by topics / Gauss Curvature

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

Academic literature on the topic 'Gauss Curvature'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 May 2022

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Journal articles on the topic "Gauss Curvature"

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Defever, Filip. "Conformally flat hypersurfaces with constant Gauss-Kronecker curvature." Bulletin of the Australian Mathematical Society 61, no. 2 (April 2000): 207–16. http://dx.doi.org/10.1017/s0004972700022218.

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We consider 3-dimensional conformally flat hypersurfaces of E4 with constant Gauss-Kronecker curvature. We prove that those with three different principal curvatures must necessarily have zero Gauss-Kronecker curvature.
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WANG, DAN, YAJUN YIN, JIYE WU, and ZHENG ZHONG. "THE INTERACTION POTENTIAL BETWEEN MICRO/NANO CURVED SURFACE BODY WITH NEGATIVE GAUSS CURVATURE AND AN OUTSIDE PARTICLE." Journal of Mechanics in Medicine and Biology 15, no. 06 (December 2015): 1540055. http://dx.doi.org/10.1142/s0219519415400552.

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Based on the negative exponential pair potential ([Formula: see text]), the interaction potential between curved surface body with negative Gauss curvature and an outside particle is proved to be of curvature-based form, i.e., it can be written as a function of curvatures. Idealized numerical experiments are designed to test the accuracy of the curvature-based potential. Compared with the previous results, it is confirmed that the interaction potential between curved surface body and an outside particle has a unified expression of curvatures regardless of the sign of Gauss curvature. Further, propositions below are confirmed: Highly curved surface body may induce driving forces, curvatures and the gradient of curvatures are the essential factors forming the driving forces.
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Inoguchi, Jun-ichi, Rushan Ziatdinov, and Kenjiro T. Miura. "A Note on Superspirals of Confluent Type." Mathematics 8, no. 5 (May 11, 2020): 762. http://dx.doi.org/10.3390/math8050762.

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Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function. They are generalizations of log-aesthetic curves, and other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. In this work, we study superspirals of confluent type via similarity geometry. Through a detailed investigation of the similarity curvatures of superspirals of confluent type, we find a new class of planar curves with monotone curvature in terms of Tricomi confluent hypergeometric function. Moreover, the proposed ideas will be our guide to expanding superspirals.
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Morgan, Frank. "WHAT IS... Gauss Curvature?" Notices of the American Mathematical Society 63, no. 02 (February 1, 2016): 144–45. http://dx.doi.org/10.1090/noti1333.

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Chow, Bennett, and Dong-Ho Tsai. "Nonhomogeneous Gauss Curvature Flows." Indiana University Mathematics Journal 47, no. 3 (1998): 0. http://dx.doi.org/10.1512/iumj.1998.47.1546.

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Cheng, Qing-Ming. "Curvatures of complete hypersurfaces in space forms." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 1 (February 2004): 55–68. http://dx.doi.org/10.1017/s0308210500003073.

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In this paper we investigate three-dimensional complete minimal hypersurfaces with constant Gauss-Kronecker curvature in a space form M4(c) (c ≤ 0). We prove that if the scalar curvature of a such hypersurface is bounded from below, then its Gauss-Kronecker curvature vanishes identically. Examples of complete minimal hypersurfaces which are not totally geodesic in the Euclidean space E4 and the hyperbolic space H4(c) with vanishing Gauss-Kronecker curvature are also presented. It is also proved that totally umbilical hypersurfaces are the only complete hypersurfaces with non-zero constant mean curvature and with zero quasi-Gauss-Kronecker curvature in a space form M4(c) (c ≤ 0) if the scalar curvature is bounded from below. In particular, we classify complete hypersurfaces with constant mean curvature and with constant quasi-Gauss-Kronecker curvature in a space form M4(c) (c ≤ 0) if the scalar curvature r satisfies r≥ ⅔c.
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Xu, Xingwang, and Paul C. Yang. "Remarks on prescribing Gauss curvature." Transactions of the American Mathematical Society 336, no. 2 (February 1, 1993): 831–40. http://dx.doi.org/10.1090/s0002-9947-1993-1087058-5.

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Chou, Kai-Seng, and Weifeng Wo. "On hyperbolic Gauss curvature flows." Journal of Differential Geometry 89, no. 3 (November 2011): 455–85. http://dx.doi.org/10.4310/jdg/1335207375.

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Kiessling, Michael, and Sagun Chanillo. "Surfaces with prescribed Gauss curvature." Duke Mathematical Journal 105, no. 2 (November 2000): 309–53. http://dx.doi.org/10.1215/s0012-7094-00-10525-x.

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Dursun, Uğur, and Rüya Yeğin. "Hyperbolic submanifolds with finite type hyperbolic Gauss map." International Journal of Mathematics 26, no. 02 (February 2015): 1550014. http://dx.doi.org/10.1142/s0129167x15500147.

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We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface Mn with nonzero constant mean curvature in a hyperbolic space [Formula: see text] has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space [Formula: see text] having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in [Formula: see text] has biharmonic hyperbolic Gauss map.
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Dissertations / Theses on the topic "Gauss Curvature"

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Pereira, José Ilhano da Silva. "Hipersuperfícies mínimas de R4 com curvatura de Gauss-Kronecker nula." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/27052.

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PEREIRA, José Ilhano da Silva. Hipersuperfícies mínimas de R4 com curvatura de Gauss-Kronecker nula. 2017. 44 f. Dissertação (Mestrado em Matemática) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.
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Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, Estou devolvendo a Dissertação de JOSÉ ILHANO DA SILVA PEREIRA, pois há alguns erros a serem corrigidos. Os mesmos seguem listados a seguir. 1- FOLHA DE APROVAÇÃO (substitua a folha de aprovação, por outra que não contenha as assinaturas dos membros da banca examinadora) 2- NUMERAÇÃO INDEVIDA (a numeração indevida de página que aparece na folha de aprovação deve ser retirada) 3- RESUMO (retire o recuo de parágrafo presente no resumo e no abstract) 4- PALAVRAS-CHAVE (apenas o primeiro elemento de cada palavra-chave deve começar com letra maiúscula, assim reescreva as palavras-chave como no exemplo a seguir: Hipersuperfícies mínimas) 5- SUMÁRIO (Os títulos dos capítulos principais, que aparecem no sumário e no interior do trabalho, devem estar em caixa alta (letra maiúscula). Ex.: 2 PRELIMINARES 2.1 Tensores 6 – REFERÊNCIAS (retire o conjunto de “citações” à autores que aparece no final das referências bibliográficas, pois elas fogem ao padrão ABNT para a página das referências) Atenciosamente, on 2017-10-04T17:50:58Z (GMT)
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This work does study the complete minimal hypersurfaces in the Euclidean space R4 , with Gauss-Kronecker curvature identically zero. Our main result is to prove that if f: M3 → R4 is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature boun-ded from below, then f(M3) splits as a Euclidean product L2 × R , where L2 is a complete minimal surface in R3 with Gaussian curvature bounded from below. Moreover, we show a result about the Gauss-Kronecker curvature of f, without any assumption on the scalar curvature.
Este trabalho tem como objetivo estudar as hipersuperfícies mínimas em R4, com curvatura de Gauss-Kronecker identicamente zero. Como resultado principal provamos que se f : M3 → R4 é uma hipersuperfície mínima com curvatura de Gauss-Kronecker identicamente zero, segunda forma fundamental não se anulando em nenhum ponto e curvatura escalar limitada inferiormente, então f(M3) se decompõe como um produto euclidiano do tipo L2 × R , onde L2 é uma superfície mínima de R3 com curvatura Gaussiana limitada inferiormente. Finalmente, apresentamos um resultado sobre a curvatura de Gauss-Kronecker de f sem nenhuma hipótese sobre a curvatura escalar.
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Zapata, Juan Fernando Zapata. "Hipersuperficies completas com curvatura de Gauss-Kronecker nula em esferas." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-07112013-142031/.

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Neste trabalho mostramos que hipersuperfícies completas da esfera Euclidiana S^4, com curvatura média constante e curvatura de Gauss-Kronecker nula são mínimas, sempre que o quadrado da norma da segunda forma fundamental for limitado superiormente. Além disso apresentamos uma descrisão local das hipersuperfícies mínimas e completas em S^5 com curvatura de Gauss- Kronecker nula e algumas hipóteses adicionais sobre as funções simétricas das curvaturas principais.
In this work we show that a complete hipersurface of the unitary sphere S^4, with constant mean curvature and zero Gauss-Kronecker curvature must be minimal, if the squared norm of the second fundamental form is bounded from above. Also, we present a local description for complete minimal hipersurfaces in S^5 with zero Gauss-Kronecker curvature, and some restrictions for the symmetric functions of the principal curvatures.
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Silva, Adam Oliveira da. "Sobre a aplicaÃÃo de Gauss para hipersuperfÃcies de curvatura mÃdia constante na esfera." Universidade Federal do CearÃ, 2009. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=2625.

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O objetivo desta dissertaÃÃo à apresentar um resultado similar ao Teorema de Bernstein sobre hipersuperfÃcies mÃnimas no espaÃo euclidiano, isto Ã, mostrar que tal resultado se generaliza para hipersuperfÃcies de Sn+1 com curvatura mÃdia constante, cuja aplicaÃÃo de Gauss estÃcontida em um hemis- fÃrio fechado de Sn+1 (Teorema 3.1). PorÃm, no caso em que a hipersuperfÃcie à mÃnima, utilizaremos na demonstraÃÃo deste teorema, um resultado sobre caracterizaÃÃo das hiperesferas de Sn+1 entre todas hipersuperfÃcies de Sn+1 em termos de suas imagens de Gauss (Teorema 2.1).
The objective of this dissertation is to show a similar result of Bernstein theorem about minimal hypersurfaces in Euclidian space, that is, to show that that result is generalized to hypersurfaces of Sn+1 with constant mean curvature, whose Gauss image is contained in a closed hemisphere of Sn+1(Theorem 3.1). However, in the case where the hypersurface is minimal, we will use in the proof of this theorem a result about the characterization of the hyperspheres of Sn+1 among all complete hypersurfaces in Sn+1 in terms of their Gauss images (Theorem 2.1)
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Targino, Renato Oliveira. "A Curvatura de Gauss-Kronecker de hipersuperfÃcies mÃnimas em formas espaciais 4-dimensionais." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=6672.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
Neste trabalho estudamos hipersuperfÃcies mÃnimas completas e com curvatura de Gauss-Kronecker constante em uma forma espacial Q4(c). Provamos que o Ãnfimo do valor absoluto da curvatura de Gauss-Kronecker de uma hipersuperfÃcie mÃnima completa em Q4(c); c ≤ 0; na qual a curvatura de Ricci à limitado inferiormente, à igual a zero. AlÃm disso, estudamos hipersuperfÃcies mÃnimas conexas M3 em uma forma espacial Q4(c) com curvatura de Gauss-Kronecker K constante. Para o caso c ≤ 0, provamos, por um argumento local, que se K à constante, entÃo K deve ser igual a zero. TambÃm apresentamos uma classificaÃÃo de hipersuperfÃcies completas mÃnimas em Q4 com K constante. Exemplos de hipersuperfÃcies mÃnimas que nÃo sÃo totalmente geodÃsicas no espaÃo Euclidiano e no espaÃo hiperbÃlico com curvatura de Gauss-Kronecker nula sÃo apresentados.
In this work we study complete minimal hypersurfaces with constant Gauss-Kronecker curvature in a space form Q4(c). We prove that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q4(c); c ≤ 0; whose Ricci curvature is bounded from below,is equal to zero. Futher, we study the connected minimal hypersurfaces M3 of a space form Q4(c) with constant Gauss-Kronecker curvature K. For the case c ≤ 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurface of Q4 with K constant. Examples of complete minimal hypersurfaces which are not totally geodesic in the Euclidean space R4 and the hiperbolic space H4(c) with vanishing Gauss-Kronecker curvature are also presented.
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Echeverria, Gilberto. "The polyhedral Gauss map and discrete curvature measures in geometric modelling." Thesis, Sheffield Hallam University, 2007. http://shura.shu.ac.uk/19598/.

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The Work in this thesis is concentrated on the study of discrete curvature as an important geometric property of objects, useful in describing their shape. The main focus is on the study of the methods to measure the discrete curvature on polyhedral surfaces. The curvatures associated with a polyhedral surface are concentrated around its vertices and along its edges. An existing method to evaluate the curvature at a vertex is the Angle Deficit, which also characterises vertices into flat, convex or saddle. In discrete surfaces other kinds of vertices are possible which this method cannot identify. The concept of Total Absolute Curvature (TAC) has been established to overcome this limitation, as a measure of curvature independent of the orientation of local geometry. However no correct implementation of the TAC exists for polyhedral surfaces, besides very simple cases. For two-dimensional discrete surfaces in space, represented as polygonal meshes, the TAC is measured by means of the Polyhedral Gauss Map (PGM) of vertices. This is a representation of the curvature of a vertex as an area on the surface of a sphere. Positive and negative components of the curvature of a vertex are distinguished as spherical polygons on the PGM. Core contributions of this thesis are the methods to identify these polygons and give a sign to them. The PGM provides a correct characterisation of vertices of any type, from basic convex and saddle types to complex mixed vertices, which have both positive and negative curvature in them. Another contribution is a visualisation program developed to show the PGM using 3D computer graphics. This program helps in the understanding and analysis of the results provided by the numerical computations of curvature. It also provides interactive tools to show the detailed information about the curvature of vertices. Finally a polygon simplification application is used to compare the curvature measures provided by the Angle Deficit and PGM methods. Various sample meshes are decimated using both methods and the simplified results compared with the original meshes. These experiments show how the TAC can be used to more effectively preserve the shape of an object. Several other applications that benefit in a similar way with the use of the TAC as a curvature measure are also proposed.
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Ferreira, Thiago Lucas da Silva, and 92-99320-5663. "Superfícies de translação Weingarten lineares nos espaços euclidiano e Lorentz-Minkowski." Universidade Federal do Amazonas, 2016. https://tede.ufam.edu.br/handle/tede/6458.

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In this dissertation we will present a demonstration that a linear Weingarten translation surface in Euclidean space and Lorentz-Minkowski space should have constant mean curvature or constant Gaussian curvature. The work is based on the article "Translation surfaces of linear Weingarten type" Antonio Bueno and Rafael López.
Nesta dissertação apresentaremos uma demonstração de que uma superfície de translação Weingarten linear no espaço euclidiano e no espaço Lorentz- Minkowski deve ter curvatura média constante ou curvatura de Gauss constante. O trabalho é baseado no artigo "Translation surfaces of linear Weingarten type"de Antonio Bueno e Rafael López.
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Román, Parra Carlos Patricio. "Large conformal metrics with prescribed sign-changing Gauss curvature and a critical Neumann problem." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/116845.

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Ingeniero Civil Matemático
En esta memoria se estudian dos problemas semilineales elípticos clásicos en la literatura: el problema de la curvatura Gaussiana prescrita en dimensión 2, y el problema de Lin-Ni-Takagi con exponente crítico en dimensión 3. En ambos se encuentran soluciones con reviente cuando el valor de un parámetro involucrado se aproxima a cierto valor crítico. En el primer capítulo se estudia el siguiente problema: Dada una función escalar $\kappa(x)$, suficientemente regular, definida en una variedad Riemanniana compacta $(M,g)$ de dimensión 2, se desea saber si $\kappa$ puede corresponder a la curvatura Gaussiana de $M$ para una métrica $g_1$, que es adicionalmente conforme a la métrica inicial $g$, es decir, $g_1=e^ug$ para alguna función escalar $u$ en $M$. Sea $f$ una función regular en $M$ tal que \equ{f\geq 0,\quad f\not\equiv 0, \quad \min_M f=0.} Sean $p_1,\ldots,p_n$ una colección de puntos cualesquiera en los que $f(p_i)=0$ y $D^2f(p_i)$ es no singular. Se demuestra que para todo $\la>0$ suficientemente pequeño, existe una familia de metricas conformes de tipo burbuja $g_\la=e^{u_\la}g$ tal que su curvatura Gaussiana está dada por la función que cambia de signo $K_{g_\la}=-f+\la^2$. Más aún, la familia $u_\la$ satisface \equ{u_\la(p_j)=-4\log \la -2 \log \left(\frac{1}{\sqrt2}\log \frac{1}{\la}\right)+O(1), \quad \la^2e^{u_\la}\rightharpoonup 8\pi\sum_{i=1}^n\delta_{p_i},} donde $\delta_p$ corresponde a la masa de Dirac en el punto $p$. En el segundo capítulo se considera el problema \equ{-\Delta u+\la u-u^5=0,\quad u>0 \quad \mbox{in }\Omega,\quad \ddn{u}=0\quad \mbox{on }\partial\Omega,} donde $\Omega\subset \R^3$ es un dominio acotado con frontera regular $\partial\Omega$, $\la>0$ and $\nu$ denota la normal unitaria exterior a $\partial\Omega$. Se demuestra que cuando $\la$ se apoxima por arriba a cierto valor explícitamente caracterizado en términos de funciones de Green, una familia de soluciones con reviente en un cierto punto interior del dominio existe.
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Baltazar, Halyson Irene. "Sobre a aplicaÃÃo de Gauss para hipersuperfÃcies com curvatura de ordem superior constante em esferas." Universidade Federal do CearÃ, 2009. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=2623.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Nesse trabalho iremos considerar uma hipersuperficie conexa, completa e orientÃvel da esfera unitÃria euclidiana Sn+1 com curvatura de ordem superior constante positiva. Provaremos sob certas condiÃÃes geomÃtricas, que caso a imagem da AplicaÃÃo de Gauss de M estiver contida em um hemisfÃrio fechado,entÃo M Ã uma hipersuperfÃcie totalmente umbÃlica de Sn+1 .
In this work we will consider connected, complete and orientable hyper-surface of the unit euclidean sphere Sn+1 with constant positive high order curvature. We will prove that under certain geometric conditions, if the image of the Gauss mapping of M is contained in a closed hemisphere, then M is atotally umbilic hypersurface of Sn+1.
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Daza, John Elber Gómez. "Superfícies mínimas e curvatura de gauss de conóides em espaços de finsler com (α,β) - métricas." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/3634.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
We consider(α,β)−metric F=αφ(β α), whereα is the euclidean metric,φ is a smooth positive function on a symmetric interval I=(−b0,b0) and β is a 1-form with the norm b,0 ≤bNeste trabalho consideramos (α,β)−métricas do tipo F=αφ(β α), ondeα é a métrica euclidiana,φ é uma função positiva suave sobre um intervalo simétrico I=(−b0,b0) e β é uma 1-forma de norma b,0 ≤ b < b0, sobre uma variedade de Finsler M. Estudamos superfícies mínimas nestes espaços (M,F) com respeito à forma volume de Holmes-Thompson e apresentamos uma equação que caracteriza as hipersuperfícies mínimasemumespaçogeral(α,β)−Minkowski.Mostramosqueosconóidesnoespaço tridimensional comβ na direção do eixo ˜y3 são mínimas se, e somente se, é um helicóide ou um plano, provamos também que a curvatura de Gauss do conóide em um espaço tridimensional de Randers-Minkowski pode ser positiva em superfícies mínimas. Finalmente apresentamos uma equação diferencial ordinária que caracteriza superfícies mínimas de rotação eum exemplo de superfíciemínimade rotação.
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Batista, Ricardo Alexandre [UNESP]. "Tópicos de geometria diferencial." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/94373.

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O principal objetivo deste trabalho é confeccionar um texto para alunos de gradua ção na área de Ciências Exatas e da Terra concernente ao estudo da Curvatura Gaussiana e Aplicação de Gauss, Superfícies Mínimas, Teorema Egregium de Gauss e o Teorema de Gauss- Bonnet para curvas simples fechadas
The main objective from this work is to make a text for students of graduation in the area of exact sciences and of the land concerning to the study of the Gaussian Curvature and the Gauss Map, Minimal Surfaces, Gauss's Theorem Egregium and the Gauss-Bonnet Theorem for Simple Closed Curves
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Books on the topic "Gauss Curvature"

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Almeida, Sebastião Carneiro de. Minimal hypersurfaces of S⁴ with constant Gauss-Kroenecker curvature. Recife, Brasil: Universidade Federal de Pernambuco, Centro de Ciências Exatas e da Natureza, Departamento de Matemática, 1985.

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Tretkoff, Paula. Riemann Surfaces, Coverings, and Hypergeometric Functions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0003.

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This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and notes that an automorphism of a Riemann surface is a biholomorphic map of the Riemann surface onto itself. It then describes a Riemannian metric and the Gauss-Bonnet theorem, which can be interpreted as a relation between the Gaussian curvature of a compact Riemann surface X and its Euler characteristic. It also examines the behavior of the Euler number under finite covering, along with finite subgroups of the group of fractional linear transformations PSL(2, C). Finally, it presents some basic facts about the classical Gauss hypergeometric functions of one complex variable, triangle groups acting discontinuously on one of the simply connected Riemann surfaces, and the hypergeometric monodromy group.
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Nolte, David D. Geometry on my Mind. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0005.

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This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics. Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics. Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems in chaos theory. Motion cannot exist without space—trajectories are the tracks of points, mathematical or physical, through it.
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Mann, Peter. Virtual Work & d’Alembert’s Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0013.

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This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, applied force and constraint force. Holonomic constraints and non-holonomic constraint equations are then investigated. The corresponding principles of Gauss (Gauss’s least constraint) and Jourdain are also documented and compared to d’Alembert’s approach before being generalised into the Mangeron–Deleanu principle. Kane’s equations are derived from Jourdain’s principle. The chapter closes with a detailed covering of the Gibbs–Appell equations as the most general equations in classical mechanics. Their reduction to Hamilton’s principle is examined and they are used to derive the Euler equations for rigid bodies. The chapter also discusses Hertz’s least curvature, the Gibbs function and Euler equations.
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Book chapters on the topic "Gauss Curvature"

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Casey, James. "Gauss (1777-1855)." In Exploring Curvature, 193–202. Wiesbaden: Vieweg+Teubner Verlag, 1996. http://dx.doi.org/10.1007/978-3-322-80274-3_14.

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Han, Qing, and Jia-Xing Hong. "Nonzero Gauss curvature." In Isometric Embedding of Riemannian Manifolds in Euclidean Spaces, 55–70. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/surv/130/04.

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Han, Qing, and Jia-Xing Hong. "Nonnegative Gauss curvature." In Isometric Embedding of Riemannian Manifolds in Euclidean Spaces, 87–108. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/surv/130/06.

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Han, Qing, and Jia-Xing Hong. "Nonpositive Gauss curvature." In Isometric Embedding of Riemannian Manifolds in Euclidean Spaces, 109–41. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/surv/130/07.

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Berres, Anne, Hans Hagen, and Stefanie Hahmann. "Deformations Preserving Gauss Curvature." In Mathematics and Visualization, 143–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44900-4_9.

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Han, Qing, and Jia-Xing Hong. "Gauss curvature changing sign cleanly." In Isometric Embedding of Riemannian Manifolds in Euclidean Spaces, 71–86. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/surv/130/05.

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Maurin, Krzysztof. "Gauss Inner Curvature of Surfaces." In The Riemann Legacy, 3–23. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8939-0_1.

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Hélein, Frédéric. "The Gauss-Codazzi condition." In Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems, 41–51. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8330-6_5.

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Pressley, Andrew. "Gaussian Curvature and the Gauss Map." In Elementary Differential Geometry, 147–69. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-3696-5_7.

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Hopf, Heinz. "Singularities of Surfaces with Constant Negative Gauss Curvature." In Lecture Notes in Mathematics, 174–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-39482-6_14.

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Conference papers on the topic "Gauss Curvature"

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Tang, Yan, and Qingchen Zhang. "Edge-Collapse Mesh Simplification Method Based on Gauss Curvature." In 4th IEEE Int'l Conference on Cyber, Physical and Social Computing (CPSCom). IEEE, 2011. http://dx.doi.org/10.1109/ithings/cpscom.2011.93.

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MAEDA, KEI-ICHI, YUKINORI SASAGAWA, and NOBUYOSHI OHTA. "BLACK HOLE SOLUTIONS IN STRING THEORY WITH GAUSS–BONNET CURVATURE CORRECTION." In Proceedings of the MG12 Meeting on General Relativity. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814374552_0450.

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Su, Jiu-Liang, and Zhao-Xia Wang. "Gradient estimate for closed starshaped hypersurfaces with prescribed Gauss curvature measure." In 2015 International Conference on Mechanics and Mechatronics (ICMM2015). WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814699143_0089.

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Shufang, Qiu, and Zhang Xiaoming. "An Improved Method for Image Denoising Based on Gauss Curvature and Gradient." In 2010 International Conference on Optoelectronics and Image Processing (ICOIP). IEEE, 2010. http://dx.doi.org/10.1109/icoip.2010.302.

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Dursun, U. "On minimal hypersurfaces of hyperbolic space ℍ4 with zero Gauss-Kronecker curvature." In Proceedings of the 10th International Conference on DGA2007. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790613_0008.

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Qiu, Shufang, Zewen Wang, and Biqin He. "PDE-based noise removal with geometrical mean diffusion of adaptive TV and Gauss curvature-driven diffusion." In 2011 4th International Congress on Image and Signal Processing (CISP). IEEE, 2011. http://dx.doi.org/10.1109/cisp.2011.6100308.

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CHAVES, ROSA M. B., and CLÁUDIA CUEVA CÂNDIDO. "THE GAUSS MAP OF SPACELIKE ROTATIONAL SURFACES WITH CONSTANT MEAN CURVATURE IN THE LORENTZ-MINKOWSKI SPACE." In Proceedings of the International Conference held to honour the 60th Birthday of A M Naveira. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777751_0009.

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Canu, Romain, Christophe Dumouchel, Benjamin Duret, Mohamed Essadki, Marc Massot, Thibault Ménard, Stefano Puggelli, Julien Reveillon, and François-Xavier Demoulin. "Where does the drop size distribution come from?" In ILASS2017 - 28th European Conference on Liquid Atomization and Spray Systems. Valencia: Universitat Politècnica València, 2017. http://dx.doi.org/10.4995/ilass2017.2017.4706.

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This study employs DNS of two-phase flows to enhance primary atomization understanding and modelling to beused in numerical simulation in RANS or LES framework. In particular, the work has been aimed at improving the information on the liquid-gas interface evolution available inside the Eulerian-Lagrangian Spray Atomization (ELSA) framework. Even though this approach has been successful to describe the complete liquid atomization process from the primary region to the dilute spray, major improvements are expected on the establishment of the drop size distribution (DSD). Indeed, the DSD is easily defined once the spray is formed, but its appearance and even the mathematical framework to describe its creation during the initial breakup of the continuous liquid phase in a set of individual liquid parcels is missing. This is the main aim of the present work to review proposals to achieve a continuous description of the DSD formation during the atomization process.The attention is here focused on the extraction from DNS data of the behaviour of geometrical variable of the liquid- gas interface, such as the mean and Gauss surface curvatures. A DNS database on curvature evolution has been generated. A Rayleigh-Plateau instability along a column of liquid is considered to analyse and to verify the capabilities of the code in correctly predicting the curvature distribution. A statistical analysis on the curvatures data, in terms of probability density function, was performed in order to determine the physical parameters that control the curvatures on this test case. Two different methods are presented to compute the curvature distribution and in addition, the probability to be at a given distance of the interface is studied. This approach finally links the new toolsproposed to follow the formation of the spray with the pioneering work done on scale distribution analysis.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4706
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Oliker, Vladimir. "A variational solution of the A. D. Aleksandrov problem of existence of a convex polytope with prescribed Gauss curvature." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc69-0-4.

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Singh, Vijay K., and S. K. Panda. "Linear Static and Free Vibration Analyses of Laminated Composite Spherical Shells." In ASME 2013 Gas Turbine India Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gtindia2013-3712.

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Linear static and free vibration behavior of laminated composite square base spherical shell panel has been investigated using finite element method. The present shell panel model is developed using ANSYS parametric design language code in ANSYS platform. The model is discretised using an eight nodded serendipity element (SHELL281) with six degrees of freedom per node from ANSYS element library. The responses are obtained using Gauss elimination and Block-Lanczos steps for the static and free vibration analysis, respectively. The results are computed using present developed model and the convergence test has also been done. Based on the convergence new results are obtained and compared with published results. The numerical simulations done for different parameters showing that the parameters such as thickness ratios, curvature ratios and lay up sequences have significant effect on transverse central deflections and fundamental free vibration frequencies of the shell structures.
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