Andrei Agrachev, Davide Barilari, Ugo Boscain

Comprehensive Introduction to Sub-Riemannian Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 31. Oktober 2019
• Englisch
• ISBN-13: 9781108754514
• Artikelnr.: 70911475

Autorenporträt

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.