Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Andrei Agrachev is currently a full professor at Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste. His research interests are: sub-Riemannian geometry, mathematical control theory, dynamical systems, differential geometry and topology, singularity theory and real algebraic geometry.
Inhaltsangabe
Introduction 1. Geometry of surfaces in R^3 2. Vector fields 3. Sub-Riemannian structures 4. Pontryagin extremals: characterization and local minimality 5. First integrals and integrable systems 6. Chronological calculus 7. Lie groups and left-invariant sub-Riemannian structures 8. Endpoint map and exponential map 9. 2D almost-Riemannian structures 10. Nonholonomic tangent space 11. Regularity of the sub-Riemannian distance 12. Abnormal extremals and second variation 13. Some model spaces 14. Curves in the Lagrange Grassmannian 15. Jacobi curves 16. Riemannian curvature 17. Curvature in 3D contact sub-Riemannian geometry 18. Integrability of the sub-Riemannian geodesic flow on 3D Lie groups 19. Asymptotic expansion of the 3D contact exponential map 20. Volumes in sub-Riemannian geometry 21. The sub-Riemannian heat equation Appendix. Geometry of parametrized curves in Lagrangian Grassmannians with Igor Zelenko References Index.
Introduction 1. Geometry of surfaces in R^3 2. Vector fields 3. Sub-Riemannian structures 4. Pontryagin extremals: characterization and local minimality 5. First integrals and integrable systems 6. Chronological calculus 7. Lie groups and left-invariant sub-Riemannian structures 8. Endpoint map and exponential map 9. 2D almost-Riemannian structures 10. Nonholonomic tangent space 11. Regularity of the sub-Riemannian distance 12. Abnormal extremals and second variation 13. Some model spaces 14. Curves in the Lagrange Grassmannian 15. Jacobi curves 16. Riemannian curvature 17. Curvature in 3D contact sub-Riemannian geometry 18. Integrability of the sub-Riemannian geodesic flow on 3D Lie groups 19. Asymptotic expansion of the 3D contact exponential map 20. Volumes in sub-Riemannian geometry 21. The sub-Riemannian heat equation Appendix. Geometry of parametrized curves in Lagrangian Grassmannians with Igor Zelenko References Index.
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