Sub-Riemannian Geometry (Progress in Mathematics (Boston, Mass.), Vol. 144.) - Hardcover

André Bellaïche; Jean-Jacques Risler

Hardcover

ISBN 10: 0817654763 ISBN 13: 9780817654764

Publisher: Birkhauser, 1996

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

Edition details

• Publisher: Birkhauser
• Publication date: 1996
• Language: English
• ISBN 10: 0817654763
• ISBN 13: 9780817654764
• Binding: Hardcover
• Number of pages: 393