A Tour of Subriemannian Geometries, Their Geodesics and Applications

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Peter May. Matthew Baker.

New Methods in Finsler Geometry - 24 May 2018

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Popular Features. New Releases. Notify me. Description Subriemannian geometries, also known as Carnot-Caratheodory geometries, can be viewed as limits of Riemannian geometries.

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Geometry of Optimal Control for Control-Affine Systems

They also arise in physical phenomenon involving ""geometric phases"" or holonomy. Given a subriemannian geometry, we can define the distance between two points just as in the Riemannian case, except we are only allowed to travel along the horizontal lines between two points.


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The book is devoted to the study of subriemannian geometries, their geodesics, and their applications. It starts with the simplest nontrivial example of a subriemannian geometry: the two-dimensional isoperimetric problem reformulated as a problem of finding subriemannian geodesics. Among topics discussed in other chapters of the first part of the book the author mentions an elementary exposition of Gromov's surprising idea to use subriemannian geometry for proving a theorem in discrete group theory and Cartan's method of equivalence applied to the problem of understanding invariants diffeomorphism types of distributions.

There is also a chapter devoted to open problems. The second part of the book is devoted to applications of subriemannian geometry.

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Reading the book requires introductory knowledge of differential geometry, and it can serve as a good introduction to this new, exciting area of mathematics. This book provides an introduction to and a comprehensive study of the qualitative theory of ordinary differential equations. It begins with fundamental theorems on existence, uniqueness, and initial conditions, and discusses basic principles in dynamical systems and Poincare-Bendixson theory.


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    A Tour of Subriemannian Geometries, Their Geodesics and Applications

    Other topics included are: the critical point at infinity, harmonic solutions for periodic differential equations, systems of ordinary differential equations on the torus, and structural stability for systems on two-dimensional manifolds. This books is accessible to graduate students and advanced undergraduates and is also of interest to researchers in this area. Exercises are included at the end of each chapter. Product details Format Paperback pages Dimensions Other books in this series. Print ISBN Online ISBN Print ISSN: Online ISSN: Primary MSC: 58 ; 53 ; Applied Math?

    A Tour of Subriemannian Geometries, Their Geodesics and Applications

    MAA Book? Electronic Media? Apparel or Gift: false. Online Price 1 Label: List. Online Price 1: Print Price 1 Label: List. Print Price 1: Online Price 2: Print Price 2: Online Price 3: Print Price 3: Dual Price 1 Label: List.

    A tour of subriemannian geometries, their geodesics, and applications

    Dual Price 1: Dual Price 2: Print Available to Order: true. Readership: Graduate students and research mathematicians interested in geometry and topology. Reviews: Very comprehensive and elegantly written book.

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