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

Introduction to Riemannian and Sub-Riemannian geometry

created by barilari on 17 Nov 2017
modified on 18 Nov 2017

[BibTeX]

Lecture Notes

Inserted: 17 nov 2017
Last Updated: 18 nov 2017

Pages: 525
Year: 2017
Links: Updated version at https://webusers.imj-prg.fr/~davide.barilari/Notes.php

Abstract:

Lecture notes "Introduction to Riemannian and Sub-Riemannian geometry".

New updated version 17.11.2017 (Ch. 13 added + Revision Ch. 8, 10, 20 + New sections added in Ch. 3, 12)

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 - 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 - Asymptotic expansion of the 3D contact exponential map. 19 - The volume in sub-Riemannian geometry. 20 - The sub-Riemannian heat equation.

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