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:
a [ control theory a [ classical mechanics a [ Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) a [ diffusion on manifolds a [ analysis of hypoelliptic operators a [ 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:
a [ AndrA(c) BellaAche: The tangent space in sub-Riemannian geometry a [ Mikhael Gromov: Carnot-CarathA(c)odory spaces seen from within a [ Richard Montgomery: Survey of singular geodesics a [ HA(c)ctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers a [ Jean-Michel Coron: Stabilization of controllable systems

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:
Andre Bellaiche: The tangent space in sub-Riemannian geometry Mikhael Gromov: Carnot-Caratheodory spaces seen from within Richard Montgomery: Survey of singular geodesics Hector J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers Jean-Michel Coron: Stabilization of controllable systems"