A Comprehensive Introduction To Sub Riemannian Geometry
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A Comprehensive Introduction To Sub Riemannian Geometry
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Author : Andrei Agrachev
language : en
Publisher: Cambridge University Press
Release Date : 2019-10-31
A Comprehensive Introduction To Sub Riemannian Geometry written by Andrei Agrachev and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-31 with Mathematics categories.
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
Sub Riemannian Geometry
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Author : Andre Bellaiche
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Sub Riemannian Geometry written by Andre Bellaiche and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely: control theory classical mechanics Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) diffusion on manifolds analysis of hypoelliptic operators Cauchy-Riemann (or CR) geometry. Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists: Andr Bellache: The tangent space in sub-Riemannian geometry Mikhael Gromov: Carnot-Carathodory spaces seen from within Richard Montgomery: Survey of singular geodesics Hctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers Jean-Michel Coron: Stabilization of controllable systems.
Sub Riemannian Geometry
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Author : Ovidiu Calin
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-20
Sub Riemannian Geometry written by Ovidiu Calin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Mathematics categories.
A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.
A Comprehensive Introduction To Differential Geometry
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Author : Michael Spivak
language : en
Publisher:
Release Date : 1979
A Comprehensive Introduction To Differential Geometry written by Michael Spivak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Sub Riemannian Geometry
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Author : Ovidiu Calin
language : en
Publisher:
Release Date : 2009
Sub Riemannian Geometry written by Ovidiu Calin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Electronic books categories.
A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.
Sub Riemannian Geometry And Optimal Transport
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Author : Ludovic Rifford
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-03
Sub Riemannian Geometry And Optimal Transport written by Ludovic Rifford and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-03 with Mathematics categories.
The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the existence of optimal transport maps for Lipschitz sub-Riemannian structure. The combination of geometry presented from an analytic point of view and of optimal transport, makes the book interesting for a very large community. This set of notes grew from a series of lectures given by the author during a CIMPA school in Beirut, Lebanon.
Riemannian Manifolds
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Author : John M. Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
Riemannian Manifolds written by John M. Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
A Comprehensive Introduction To Differential Geometry
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Author : Michael Spivak
language : en
Publisher:
Release Date : 1970
A Comprehensive Introduction To Differential Geometry written by Michael Spivak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Riemannian Geometry
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Author : Isaac Chavel
language : en
Publisher: Cambridge University Press
Release Date : 2006-04-10
Riemannian Geometry written by Isaac Chavel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-10 with Mathematics categories.
This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.
Introduction To Differential Geometry And Riemannian Geometry
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Author : Erwin Kreyszig
language : en
Publisher:
Release Date : 1968-12-15
Introduction To Differential Geometry And Riemannian Geometry written by Erwin Kreyszig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968-12-15 with Education categories.
This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space and to n-dimensional Riemannian geometry. Based on Kreyszig's earlier book Differential Geometry, it is presented in a simple and understandable manner with many examples illustrating the ideas, methods, and results. Among the topics covered are vector and tensor algebra, the theory of surfaces, the formulae of Weingarten and Gauss, geodesics, mappings of surfaces and their applications, and global problems. A thorough investigation of Reimannian manifolds is made, including the theory of hypersurfaces. Interesting problems are provided and complete solutions are given at the end of the book together with a list of the more important formulae. Elementary calculus is the sole prerequisite for the understanding of this detailed and complete study in mathematics.