Ebook: Sub-Riemannian Geometry
- Tags: Differential Geometry, Global Analysis and Analysis on Manifolds
- Series: Progress in Mathematics 144
- Year: 1996
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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:
• André Bellaïche: The tangent space in sub-Riemannian geometry • Mikhael Gromov: Carnot-Carathéodory spaces seen from within • Richard Montgomery: Survey of singular geodesics • Héctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers • 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:
• 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
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
Content:
Front Matter....Pages i-viii
The tangent space in sub-Riemannian geometry....Pages 1-78
Carnot-Carath?odory spaces seen from within....Pages 79-323
Survey of singular geodesics....Pages 325-339
A cornucopia of four-dimensional abnormal sub-Riemannian minimizers....Pages 341-364
Stabilization of controllable systems....Pages 365-388
Back Matter....Pages 389-394
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
Content:
Front Matter....Pages i-viii
The tangent space in sub-Riemannian geometry....Pages 1-78
Carnot-Carath?odory spaces seen from within....Pages 79-323
Survey of singular geodesics....Pages 325-339
A cornucopia of four-dimensional abnormal sub-Riemannian minimizers....Pages 341-364
Stabilization of controllable systems....Pages 365-388
Back Matter....Pages 389-394
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