A COMPREHENSIVE INTRODUCTION TO SUB-RIEMANNIAN GEOMETRY

The lecture notes previously posted on this page have been accepted for publication for Cambridge University Press

with the title "A Comprehensive Introduction to Sub-Riemannian Geometry"

Final draft version Feb 06, 2019 [643 pp.] (download .pdf) (download .djvu)

For old versions (click here)

Preprint SISSA 09/2012/M

The lecture notes previously posted on this page have been accepted for publication for Cambridge University Press

with the title "A Comprehensive Introduction to Sub-Riemannian Geometry"

Final Table of Contents: (download available below)

- Chapter 1 - Geometry of surfaces in R^3.
- Chapter 2 - Vector fields.
- Chapter 3 - Sub-Riemannian structures.
- Chapter 4 - Characterization and local minimality of Pontryagin extremals.
- Chapter 5 - First integrals and integrable systems.
- Chapter 6 - Chronological calculus.
- Chapter 7 - Lie groups and left-invariant sub-Riemannian structures.
- Chapter 8 - End-point map and exponential map.
- Chapter 9 - 2D Almost-Riemannian structures.
- Chapter 10 - Nonholonomic tangent space.
- Chapter 11 - Regularity of the sub-Riemannian distance.
- Chapter 12 - Abnormal extremals and second variation.
- Chapter 13 - Some model spaces.
- Chapter 14 - Curves in the Lagrange Grassmannian.
- Chapter 15 - Jacobi curves.
- Chapter 16 - Riemannian curvature.
- Chapter 17 - Curvature of 3D contact sub-Riemannian structures and applications.
- Chapter 18 - Integrability of the sub-Riemannian geodesic flow on 3D Lie groups.
- Chapter 19 - Asymptotic expansion of the 3D contact exponential map.
- Chapter 20 - The volume in sub-Riemannian geometry.
- Chapter 21 - The sub-Riemannian heat equation.
- Appendix - Geometry of parametrized curves in Lagrange Grassmannian (written by Igor Zelenko).

Final draft version Feb 06, 2019 [643 pp.] (download .pdf) (download .djvu)

For old versions (click here)

Preprint SISSA 09/2012/M

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