Sub-Riemannian geometry has been a full research domain, with motivations and ramifications in several parts of pure and applied mathematics. This book provides an introduction to sub-Riemannian geometry. Editor(s): Bass, Hyman; Risler, Jean-Jaques. Series: Progress in Mathematics. Num Pages: 398 pages, biography. BIC Classification: PBMP. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 23. Weight in Grams: 752. . 1996. 1996th Edition. hardcover. . . . . Books ship from the US and Ireland.

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Bibliographic Details

Title: Sub-Riemannian Geometry
Publisher: Birkhauser Verlag AG
Publication Date: 1996
Language: English
ISBN 10: 3764354763
ISBN 13: 9783764354763
Binding: Hardcover
Condition: New

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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:
• Andr� Bella�che: The tangent space in sub-Riemannian geometry • Mikhael Gromov: Carnot-Carath�odory spaces seen from within • Richard Montgomery: Survey of singular geodesics • H�ctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers • Jean-Michel Coron: Stabilization of controllable systems

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