A tour of subriemannian geometries, their geodesics and applications. (English) Zbl 1044.53022

Mathematical Surveys and Monographs 91. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-1391-9/hbk). xx, 259 p. (2002).
From the introduction: A sub-Riemannian geometry is a manifold endowed with a distribution and a fiber inner product on the distribution. This book is a study of these geometries, focusing on their geodesics and their applications.


53C17 Sub-Riemannian geometry
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70H05 Hamilton’s equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems