Book Description
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
Author : Andrei Agrachev
Publisher : Cambridge University Press
Page : 765 pages
File Size : 28,89 MB
Release : 2019-10-31
Category : Mathematics
ISBN : 110847635X
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
Author : Ludovic Rifford
Publisher : Springer Science & Business Media
Page : 146 pages
File Size : 50,1 MB
Release : 2014-04-03
Category : Mathematics
ISBN : 331904804X
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.
Author : Andrei Agrachev
Publisher : Cambridge University Press
Page : 765 pages
File Size : 32,87 MB
Release : 2019-10-31
Category : Mathematics
ISBN : 1108757251
Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several areas of pure and applied mathematics, with applications to many areas such as quantum control, Hamiltonian dynamics, robotics and Lie theory. This comprehensive introduction proceeds from classical topics to cutting-edge theory and applications, assuming only standard knowledge of calculus, linear algebra and differential equations. The book may serve as a basis for an introductory course in Riemannian geometry or an advanced course in sub-Riemannian geometry, covering elements of Hamiltonian dynamics, integrable systems and Lie theory. It will also be a valuable reference source for researchers in various disciplines.
Author : Andre Bellaiche
Publisher : Birkhäuser
Page : 404 pages
File Size : 45,74 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034892101
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.
Author : Leonor Godinho
Publisher : Springer
Page : 476 pages
File Size : 22,14 MB
Release : 2014-07-26
Category : Mathematics
ISBN : 3319086669
Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.
Author : Luca Capogna
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 22,10 MB
Release : 2007-08-08
Category : Mathematics
ISBN : 3764381337
This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.
Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 39,1 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387227261
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.
Author : John M. Lee
Publisher : Springer
Page : 447 pages
File Size : 24,91 MB
Release : 2019-01-02
Category : Mathematics
ISBN : 3319917552
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.
Author :
Publisher : Academic Press
Page : 441 pages
File Size : 21,82 MB
Release : 1975-08-22
Category : Mathematics
ISBN : 0080873790
An Introduction to Differentiable Manifolds and Riemannian Geometry
Author : Isaac Chavel
Publisher : Cambridge University Press
Page : 402 pages
File Size : 22,44 MB
Release : 1995-01-27
Category : Mathematics
ISBN : 9780521485784
This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.