Calculus of Variations and Geometric Measure Theory
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A. Agrachev - D. Barilari - U. Boscain

A Comprehensive Introduction to Sub-Riemannian Geometry

created by barilari on 17 Nov 2017
modified on 15 Mar 2019

[BibTeX]

Lecture Notes

Inserted: 17 nov 2017
Last Updated: 15 mar 2019

Journal: Cambridge Studies in Advanced Mathematics
Year: 2019
Links: Link at publisher

Abstract:

These lecture notes have been accepted for publication for Cambridge University Press with the title "A Comprehensive Introduction to Sub-Riemannian Geometry", in the series Cambridge Studies in Advanced Mathematics

Table of Contents: 1 - Geometry of surfaces in R3. 2 - Vector fields and vector bundle. 3 - Sub-Riemannian structures. 4 - Characterization and local minimality of Pontryagin extremals. 5 - First integrals and Integrable systems. 6 - Chronological calculus. 7 - Lie groups and left-invariant sub-Riemannian structures 8 - End-point 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 of 3D contact sub-Riemannian structures. 18 - Integrability of the sub-Riemannian geodesic flow on 3D Lie groups. 19 - Asymptotic expansion of the 3D contact exponential map. 20 - The volume in sub-Riemannian geometry. 21 - The sub-Riemannian heat equation.

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