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.
Geometric Control Theory And Sub Riemannian Geometry
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Author : Gianna Stefani
language : en
Publisher: Springer
Release Date : 2014-06-05
Geometric Control Theory And Sub Riemannian Geometry written by Gianna Stefani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Mathematics categories.
Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.
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.
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.
Sub Riemannian Geometry
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Author : Jean-Jacques Risler
language : en
Publisher: Birkhauser
Release Date : 1996-01-01
Sub Riemannian Geometry written by Jean-Jacques Risler and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Global differential geometry 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.
Geometry Analysis And Dynamics On Sub Reimannian Manifolds
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Author : Davide Barilari
language : en
Publisher: European Mathematical Society
Release Date : 2016
Geometry Analysis And Dynamics On Sub Reimannian Manifolds written by Davide Barilari and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Geometry, Differential categories.
In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology. The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students.
Geometry Analysis And Dynamics On Sub Reimannian Manifolds
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Author : Davide Barilari
language : en
Publisher:
Release Date : 2016
Geometry Analysis And Dynamics On Sub Reimannian Manifolds written by Davide Barilari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with MATHEMATICS categories.
Control Of Nonholonomic Systems From Sub Riemannian Geometry To Motion Planning
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Author : Frédéric Jean
language : en
Publisher: Springer
Release Date : 2014-07-17
Control Of Nonholonomic Systems From Sub Riemannian Geometry To Motion Planning written by Frédéric Jean and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-17 with Science categories.
Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.