Sub-Riemannian Geometry

Bellaiche, Andre (EDT); Risler, Jean-Jacques (EDT)

ISBN 10: 3764354763 / ISBN 13: 9783764354763

Published by Birkhäuser, 1996

Seller Inventory # 4383226-n

Synopsis:

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: • André Bellaïche: The tangent space in sub-Riemannian geometry • Mikhael Gromov: Carnot-Carathéodory spaces seen from within • Richard Montgomery: Survey of singular geodesics • Héctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers • Jean-Michel Coron: Stabilization of controllable systems

Synopsis: This work provides an introduction to sub-Riemannian geometry and presents up-to-date problems in the field.

Bibliographic Details

Title: Sub-Riemannian Geometry
Publisher: Birkhäuser
Publication Date: 1996
Binding: Hardcover
Condition: New