{"title": "Sub-Riemannian Geometry", "covers": [9370717], "key": "/works/OL20695453W", "authors": [{"type": {"key": "/type/author_role"}, "author": {"key": "/authors/OL7857907A"}}], "type": {"key": "/type/work"}, "subjects": ["Differential Geometry", "Mathematics", "Global analysis", "Global differential geometry", "Global Analysis and Analysis on Manifolds"], "description": {"type": "/type/text", "value": "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: \u2022 control theory \u2022 classical mechanics \u2022 Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) \u2022 diffusion on manifolds \u2022 analysis of hypoelliptic operators \u2022 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: \u2022 Andr\u00e9 Bella\u00efche: The tangent space in sub-Riemannian geometry \u2022 Mikhael Gromov: Carnot-Carath\u00e9odory spaces seen from within \u2022 Richard Montgomery: Survey of singular geodesics \u2022 H\u00e9ctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers \u2022 Jean-Michel Coron: Stabilization of controllable systems"}, "latest_revision": 2, "revision": 2, "created": {"type": "/type/datetime", "value": "2020-05-01T11:48:24.650528"}, "last_modified": {"type": "/type/datetime", "value": "2024-09-28T22:22:58.702928"}}