A comprehensive introduction to sub-Riemannian geometry from the Hamiltonian viewpoint

Cover......Page 1
Front Matter......Page 3
CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS......Page 5
A Comprehensive Introduction to Sub-Riemannian Geometry: From the Hamiltonian Viewpoint......Page 7
Copyright......Page 8
Dedication......Page 9
Contents......Page 11
Preface......Page 21
Introduction......Page 23
1 Geometry of Surfaces in R3......Page 33
2 Vector Fields......Page 67
3 Sub-Riemannian Structures......Page 89
4 Pontryagin Extremals: Characterization andLocal Minimality......Page 131
5 First Integrals and Integrable Systems......Page 171
6 Chronological Calculus......Page 193
7 Lie Groups and Left-InvariantSub-Riemannian Structures......Page 213
8 Endpoint Map and Exponential Map......Page 268
9 2D Almost-Riemannian Structures......Page 317
10 Nonholonomic Tangent Space......Page 353
11 Regularity of the Sub-Riemannian Distance......Page 398
12 Abnormal Extremals and Second Variation......Page 424
13 Some Model Spaces......Page 478
14 Curves in the Lagrange Grassmannian......Page 535
15 Jacobi Curves......Page 564
16 Riemannian Curvature......Page 573
17 Curvature in 3D ContactSub-Riemannian Geometry......Page 593
18 Integrability of the Sub-Riemannian GeodesicFlow on 3D Lie Groups......Page 629
19 Asymptotic Expansion of the 3D ContactExponential Map......Page 655
20 Volumes in Sub-Riemannian Geometry......Page 676
21 The Sub-Riemannian Heat Equation......Page 696
Appendix.  Geometry of Parametrized Curves in Lagrangian Grassmannians......Page 720
References......Page 747
Index......Page 762