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Sub-Riemannian Geometry
Hardcover
Series: Progress in Mathematics, Book 144
ISBN13: 9783764354763
Publisher: Springer Nature
Published: Sep 26 1996
Pages: 398
Weight: 1.66
Height: 0.94 Width: 6.14 Depth: 9.21
Language: English
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.
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
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