Progress in Mathematics

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