Littérature scientifique sur le sujet « Sub-Riemannian manifold »
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Articles de revues sur le sujet "Sub-Riemannian manifold"
Falbel, Elisha, Claudio Gorodski et Michel Rumin. « Holonomy of Sub-Riemannian Manifolds ». International Journal of Mathematics 08, no 03 (mai 1997) : 317–44. http://dx.doi.org/10.1142/s0129167x97000159.
Texte intégralTan, Kang-Hai, et Xiao-Ping Yang. « On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds ». Bulletin of the Australian Mathematical Society 70, no 2 (octobre 2004) : 177–98. http://dx.doi.org/10.1017/s0004972700034407.
Texte intégralAgrachev, Andrei, Ugo Boscain, Robert Neel et Luca Rizzi. « Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling ». ESAIM : Control, Optimisation and Calculus of Variations 24, no 3 (2018) : 1075–105. http://dx.doi.org/10.1051/cocv/2017037.
Texte intégralBEJANCU, AUREL. « A LINEAR CONNECTION FOR BOTH SUB-RIEMANNIAN GEOMETRY AND NONHOLONOMIC MECHANICS (I) ». International Journal of Geometric Methods in Modern Physics 08, no 04 (juin 2011) : 725–52. http://dx.doi.org/10.1142/s0219887811005361.
Texte intégralHan, Yanling, Fengyun Fu et Peibiao Zhao. « On semi-symmetric metric connection in sub-Riemannian manifold ». Tamkang Journal of Mathematics 47, no 4 (30 décembre 2016) : 373–84. http://dx.doi.org/10.5556/j.tkjm.47.2016.1908.
Texte intégralHan, Yanling, Fengyun Fu et Peibiao Zhao. « A class of non-holonomic projective connections on sub-Riemannian manifolds ». Filomat 31, no 5 (2017) : 1295–303. http://dx.doi.org/10.2298/fil1705295h.
Texte intégralGalaev, S. « On geometry of sub-Riemannian η-Einstein manifolds ». Differential Geometry of Manifolds of Figures, no 50 (2018) : 68–81. http://dx.doi.org/10.5922/10.5922/0321-4796-2019-50-9.
Texte intégralRovenski, Vladimir. « Integral Formulas for a Foliation with a Unit Normal Vector Field ». Mathematics 9, no 15 (26 juillet 2021) : 1764. http://dx.doi.org/10.3390/math9151764.
Texte intégralRovenski, Vladimir. « Geometric Inequalities for a Submanifold Equipped with Distributions ». Mathematics 10, no 24 (14 décembre 2022) : 4741. http://dx.doi.org/10.3390/math10244741.
Texte intégralDATTA, MAHUYA. « PARTIAL ISOMETRIES OF A SUB-RIEMANNIAN MANIFOLD ». International Journal of Mathematics 23, no 02 (février 2012) : 1250043. http://dx.doi.org/10.1142/s0129167x12500437.
Texte intégralThèses sur le sujet "Sub-Riemannian manifold"
Giovannardi, Gianmarco. « Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex ». Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/11473/.
Texte intégralWhiting, James K. (James Kalani) 1980. « Path optimization using sub-Riemannian manifolds with applications to astrodynamics ». Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/63035.
Texte intégralCataloged from PDF version of thesis.
Includes bibliographical references (p. 131).
Differential geometry provides mechanisms for finding shortest paths in metric spaces. This work describes a procedure for creating a metric space from a path optimization problem description so that the formalism of differential geometry can be applied to find the optimal paths. Most path optimization problems will generate a sub-Riemannian manifold. This work describes an algorithm which approximates a sub-Riemannian manifold as a Riemannian manifold using a penalty metric so that Riemannian geodesic solvers can be used to find the solutions to the path optimization problem. This new method for solving path optimization problems shows promise to be faster than other methods, in part because it can easily run on parallel processing units. It also provides some geometrical insights into path optimization problems which could provide a new way to categorize path optimization problems. Some simple path optimization problems are described to provide an understandable example of how the method works and an application to astrodynamics is also given.
by James K. Whiting.
Ph.D.
Tashiro, Kenshiro. « Gromov-Hausdorff limits of compact Heisenberg manifolds with sub-Riemannian metrics ». Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263433.
Texte intégralWang, Jing. « Sub-Riemannian heat kernels on model spaces and curvature-dimension inequalities on contact manifolds ». Thesis, Purdue University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3636683.
Texte intégralThis dissertation contains two research directions. In the first direction, we deduce explicit expressions of the subelliptic heat kernels on three sub-Riemannian model spaces: the Cauchy-Riemann sphere, the anti-de Sitter space and the Quaternionic sphere. From these explicit subelliptic heat kernels we then derive several by products: the Green function of the conformal sub-Laplacian, the small-time estimates of the subel- liptic heat kernels, and the sub-Riemannian distance. The key point is to work in cylindrical coordinates that reflect the symmetries coming from the Hopf fibration of these model spaces. In the second direction we study the extension of the Baudoin-Garofalo type curvature dimension inequality from the sub-Riemannian transversal symmetric setting to any contact manifold. In particular, the Sasakian condition is no longer assumed which leads to the appearance of new strongly non-linear term in the curvature dimension inequality. This new curvature dimension condition is then used to study several interesting aspects in geometry and analysis: The stochastic completeness of the heat semigroup, geometric conditions ensuring the compactness of the underlying manifold (Bonnet-Myers type results), gradient bounds for the heat semigroup, and spectral gap estimates for the sub-Laplacian.
Kokkonen, Petri. « Étude du modèle des variétés roulantes et de sa commandabilité ». Thesis, Paris 11, 2012. http://www.theses.fr/2012PA112317/document.
Texte intégralWe study the controllability of the control system describing the rolling motion, without slipping nor spinning, of two n-dimensional Riemannian manifolds, one against the other.This model is closely related to the concepts of development and holonomy of the manifolds, and it generalizes to the case of affine manifolds.The main contributions are those given in four articles attached to the the thesis.First of them "Rolling manifolds and Controllability: the 3D case"deal with the case where the two manifolds are 3-dimensional. We give the listof all the possible cases for which the system is not controllable.In the second paper "Rolling manifolds on space forms"one of the manifolds is assumed to have constant curvature.We can then reduce the study of controllability to the study of the holonomy groupof a certain vector bundle connection and we show, for example, thatif the manifold with the constant curvature is an n-sphere and ifthis holonomy group does not act transitively,then the other manifold is in fact isometric to the sphere.The third paper "A Characterization of Isometries between Riemannian Manifolds by using Development along Geodesic Triangles"describes, by using the rolling motion (or development) along the loops,an alternative version of the Cartan-Ambrose-Hicks Theorem,which characterizes, among others, the Riemannian isometries.More precisely, we prove that if one starts from a certain initial orientation,and if one only rolls along loops based at the initial point (associated to this orientation),then the two manifolds are isometric if (and only if) the pathstraced by the rolling motion on the other manifolds, are all loops.Finally, the fourth paper "Rolling Manifolds without Spinning"studies the rolling motion, and its controllability, when slipping is allowed.We characterize the structure of all the possible orbits in terms of the holonomy groupsof the manifolds in question. It is also shown that there does not exist anyprincipal bundle structure such that the related distribution becomes a principal distribution,a fact that is to be compared especially to the results of the second article.Furthermore, in the third chapter of the thesis, we construct carefully the rolling modelin the more general framework of affine manifolds, as well as that of Riemannian manifolds,of possibly different dimensions
Hafassa, Boutheina. « Deux problèmes de contrôle géométrique : holonomie horizontale et solveur d'esquisse ». Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS017/document.
Texte intégralWe study two problems arising from geometric control theory. The Problem I consists of extending the concept of horizontal holonomy group for affine manifolds. More precisely, we consider a smooth connected finite-dimensional manifold M, an affine connection ∇ with holonomy group H∇ and ∆ a smooth completely non integrable distribution. We define the ∆-horizontal holonomy group H∆∇ as the subgroup of H∇ obtained by ∇-parallel transporting frames only along loops tangent to ∆. We first set elementary properties of H∆∇ and show how to study it using the rolling formalism. In particular, it is shown that H∆∇ is a Lie group. Moreover, we study an explicit example where M is a free step-two homogeneous Carnot group with m≥2 generators, and ∇ is the Levi-Civita connection associated to a Riemannian metric on M, and show in this particular case that H∆∇ is compact and strictly included in H∇ as soon as m≥3. The Problem II is studying the modeling of the problem of solver sketch. This problem is one of the steps of a CAD/CAM software. Our goal is to achieve a well founded mathematical modeling and systematic the problem of solver sketch. The next step is to understand the convergence of the algorithm, to improve the results and to expand the functionality. The main idea of the algorithm is to replace first the points of the space of spheres by displacements (elements of the group) and then use a Newton's method on Lie groups obtained. In this thesis, we classified the possible displacements of the groups using the theory of Lie groups. In particular, we distinguished three sets, each set containing an object type: the first one is the set of points, denoted Points, the second is the set of lines, denoted Lines, and the third is the set of circles and lines, we note that ∧. For each type of object, we investigated all the possible movements of groups, depending on the desired properties. Finally, we propose to use the following displacement of groups for the displacement of points, the group of translations, which acts transitively on Lines ; for the lines, the group of translations and rotations, which is 3-dimensional and acts transitively (globally but not locally) on Lines ; on lines and circles, the group of anti-translations, rotations and dilations which has dimension 4 and acts transitively (globally but not locally) on ∧
Giovannardi, Gianmarco. « Variations for submanifolds of fixed degree ». Doctoral thesis, 2020. https://hdl.handle.net/2158/1287865.
Texte intégralSubils, Mauro. « El problema de equivalencia y la prolongación de Tanaka para distribuciones totalmente no integrables ». Doctoral thesis, 2015. http://hdl.handle.net/11086/2789.
Texte intégralEsta tesis trata del Problema de Equivalencia para distribuciones y estructuras geométricas asociadas, o sub-estructuras. Repasamos el método de equivalencia de Cartan y lo comparamos con el Método de Prolongación de Tanaka, que refina ese para estructuras asociadas a distribuciones. Damos una breve introducción a las conexiones de Cartan, que es lo se aspira obtener al resolver un Problema de Equivalencia, y obtenemos algunos resultados sobre su existencia y unicidad. Finalmente, aplicamos la prolongación de Tanaka geométrica a ejemplos distinguidos de distribuciones con métricas subriemannianas y subconformes, obteniendo sus conexiones de Cartan normales y sus invariantes fundamentales.
Livres sur le sujet "Sub-Riemannian manifold"
Barilari, Davide, Ugo Boscain et Mario Sigalotti, dir. Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Zuerich, Switzerland : European Mathematical Society Publishing House, 2016. http://dx.doi.org/10.4171/162.
Texte intégralBarilari, Davide, Ugo Boscain et Mario Sigalotti, dir. Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Zuerich, Switzerland : European Mathematical Society Publishing House, 2016. http://dx.doi.org/10.4171/163.
Texte intégralE, Chang Der-chen, dir. Sub-Riemannian geometry : General theory and examples. Cambridge : Cambridge University Press, 2009.
Trouver le texte intégralCalin, Ovidiu, et Der-Chen Chang. Sub-Riemannian Geometry : General Theory and Examples. Cambridge University Press, 2013.
Trouver le texte intégralCalin, Ovidiu, et Der-Chen Chang. Sub-Riemannian Geometry : General Theory and Examples. Cambridge University Press, 2013.
Trouver le texte intégralCalin, Ovidiu, et Der-Chen Chang. Sub-Riemannian Geometry : General Theory and Examples. Cambridge University Press, 2009.
Trouver le texte intégralGauthier, Jean-Paul, Ugo Boscain, Andrey Sarychev, Gianna Stefani et Mario Sigalotti. Geometric Control Theory and Sub-Riemannian Geometry. Springer London, Limited, 2014.
Trouver le texte intégralGeometric Control Theory and Sub-Riemannian Geometry. Springer, 2014.
Trouver le texte intégralGauthier, Jean-Paul, Ugo Boscain, Andrey Sarychev, Gianna Stefani et Mario Sigalotti. Geometric Control Theory and Sub-Riemannian Geometry. Springer International Publishing AG, 2016.
Trouver le texte intégralDanielli, Donatella, Luca Capogna, Scott D. Pauls et Jeremy Tyson. Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem. Birkhauser Verlag, 2007.
Trouver le texte intégralChapitres de livres sur le sujet "Sub-Riemannian manifold"
Sverdlov, Roman, et Dimiter Vassilev. « On Sub-Riemannian and Riemannian Spaces Associated to a Lorentzian Manifold ». Dans Trends in Mathematics, 503–11. Cham : Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87502-2_51.
Texte intégralMarkina, Irina, et Stephan Wojtowytsch. « On the Alexandrov Topology of sub-Lorentzian Manifolds ». Dans Geometric Control Theory and Sub-Riemannian Geometry, 287–311. Cham : Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02132-4_17.
Texte intégralGhezzi, Roberta, et Frédéric Jean. « Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds ». Dans Geometric Control Theory and Sub-Riemannian Geometry, 201–18. Cham : Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02132-4_13.
Texte intégralBaudoin, Fabrice. « Geometric Inequalities on Riemannian and Sub-Riemannian Manifolds by Heat Semigroups Techniques ». Dans Lecture Notes in Mathematics, 7–91. Cham : Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-84141-6_2.
Texte intégralPesenson, Isaac. « Parseval Space-Frequency Localized Frames on Sub-Riemannian Compact Homogeneous Manifolds ». Dans Frames and Other Bases in Abstract and Function Spaces, 413–33. Cham : Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55550-8_17.
Texte intégralAtçeken, Mehmet, Ümit Yildirim et Süleyman Dirik. « Sub-Manifolds of a Riemannian Manifold ». Dans Manifolds - Current Research Areas. InTech, 2017. http://dx.doi.org/10.5772/65948.
Texte intégral« Sub-Riemannian Geometry, Heisenberg Manifolds and Quantum Mechanics of Landau Levels ». Dans Applications of Contact Geometry and Topology in Physics, 99–130. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814412094_0006.
Texte intégralActes de conférences sur le sujet "Sub-Riemannian manifold"
Liu, Sidun, Peng Qiao, Yong Dou et Ruochun Jin. « Searching Latent Sub-Goals in Hierarchical Reinforcement Learning as Riemannian Manifold Optimization ». Dans 2022 IEEE International Conference on Multimedia and Expo (ICME). IEEE, 2022. http://dx.doi.org/10.1109/icme52920.2022.9859878.
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