Sub-Riemannian Geometry: 144 (Progress in Mathematics, 144) - Hardcover

 
9783764354763: Sub-Riemannian Geometry: 144 (Progress in Mathematics, 144)

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" may belong to another edition of this title.

Synopsis

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

"About this title" may belong to another edition of this title.

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9783034899468: Sub-Riemannian Geometry: 144 (Progress in Mathematics, 144)

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ISBN 10:  3034899467 ISBN 13:  9783034899468
Publisher: Birkhäuser, 2011
Softcover