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A Tour of Subriemannian Geometries, Their Geodesics and Applications
About this Title
Richard Montgomery, University of California, Santa Cruz, CA
Publication: Mathematical Surveys and Monographs
Publication Year:
2002; Volume 91
ISBNs: 978-0-8218-4165-5 (print); 978-1-4704-1318-7 (online)
DOI: https://doi.org/10.1090/surv/091
MathSciNet review: MR1867362
MSC: Primary 53C17; Secondary 37J99, 53C60, 58E10, 70G45, 70H05
Table of Contents
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Front/Back Matter
Part 1. Geodesies in subriemannian manifolds
- 1. Dido meets Heisenberg
- 2. Chow’s theorem: Getting from A to B
- 3. A remarkable horizontal curve
- 4. Curvature and nilpotentization
- 5. Singular curves and geodesics
- 6. A zoo of distributions
- 7. Cartan’s approach
- 8. The tangent cone and Carnot groups
- 9. Discrete groups tending to Carnot geometries
- 10. Open problems
Part 2. Mechanics and geometry of bundles
- 11. Metrics on bundles
- 12. Classical particles in yang-mills fields
- 13. Quantum phases
- 14. Falling, swimming, and orbiting
Part 3. Appendices
- Appendix A. Geometric mechanics
- Appendix B. Bundles and the Hopf fibration
- Appendix C. The Sussmann and Ambrose-Singer Theorems
- Appendix D. Calculus of the endpoint map and existence of geodesies