A Comprehensive Introduction to Sub-Riemannian Geometry

Andrei Agrachev, Davide Barilari, Ugo Boscain

ISBN 10: 110847635X / ISBN 13: 9781108476355

Published by Cambridge University Press, GB, 2019

About this Item

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.

Seller Inventory # LU-9781108476355

Bibliographic Details

• Title: A Comprehensive Introduction to Sub-Riemannian Geometry
• Publisher: Cambridge University Press, GB
• Publication Date: 2019
• Language: English
• ISBN 10: 110847635X
• ISBN 13: 9781108476355
• Binding: Hardback
• Condition: New
• Weight: 1190 grams

About this title

Synopsis

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.

About the Authors

Andrei Agrachev is currently a full professor at Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste. His research interests are: sub-Riemannian geometry, mathematical control theory, dynamical systems, differential geometry and topology, singularity theory and real algebraic geometry.

Davide Barilari is Maître de Conférence at Université de Paris VII (Denis Diderot). His research interests are: sub-Riemannian geometry, hypoelliptic operators, curvature and optimal transport.

Ugo Boscain is Research Director at Centre National de la Recherche Scientifique (CNRS), Paris. His research interests are: sub-Riemannian geometry, hypoelliptic operators, quantum mechanics, singularity theory and geometric control.