Sub-Riemannian geometry : general theory and examples
Author(s)
Bibliographic Information
Sub-Riemannian geometry : general theory and examples
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, [126]）
Cambridge University Press, 2009
- Other Title
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Subriemannian geometry
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. 363-366) and index
Description and Table of Contents
Description
Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry.
Table of Contents
- Part I. General Theory: 1. Introductory chapter
- 2. Basic properties
- 3. Horizontal connectivity
- 4. Hamilton-Jacobi theory
- 5. Hamiltonian formalism
- 6. Lagrangian formalism
- 7. Connections on sub-Riemannian manifolds
- 8. Gauss' theory of sub-Riemannian manifolds
- Part II. Examples and Applications: 9. Heisenberg manifolds
- 10. Examples of Heisenberg manifolds
- 11. Grushin manifolds
- 12. Hormander manifolds
- Appendix A: local non-solvability
- Appendix B: fibre bundles.
by "Nielsen BookData"
