Comprehensive Introduction to Sub-Riemannian Geometry
Comprehensive Introduction to Sub-Riemannian Geometry
; ;
Cambridge University Press
10/2019
762
Dura
Inglês
9781108476355
Descrição não disponível.
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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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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
