MENU

You are here

Introduction to Sub-Riemannian geometry

Lecturer: 
Course Type: 
PhD Course
Academic Year: 
2014-2015
Period: 
January-April
Duration: 
60 h
Description: 

 1. Isoperimetric problem and Heisenberg group.

 2. Sub-Riemannian length and metric.

 3. Rashevskii-Chow theorem.

 4. Existence of length-minimizers.

 5. Normal and abnormal geodesics.

 6. Hamiltonian setting; Hamiltonian characterization of geodesics.

 7. The endpoint map and the exponential map; conjugate and cut points.

 8. Nonholonomic tangent space.

 9. Popp volume and Hausdorff measure.

10. Sub-Laplacian and sub-Riemannian heat equation. 

11. Lie groups and left-invariant sub-Riemannian structures.

12. Low-dimensional models.

13. Analytic properties of the Carnot-Caratheodory distance.

14. Second variation and Jacobi curves.

15. Sub-Riemannian curvature.

Location: 
A-133
Next Lectures: 

Sign in