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
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