Research and Lecture notes

In this lecture we cover some basic results about the theory of Lie groups.

We present some relations between curvature bounds and properties of the fundamental group of a manifold.

In this lecture we present some classical applications of curvature bounds.

In this lecture we introduce the sectional, Ricci and scalar curvatures of Riemannian manifolds.

This is the second lecture about the study of Riemannian manifolds as metric spaces.

In this lecture we study Riemannian manifolds as metric spaces.

This lecture deals with densities and distances on Riemannian manifolds.

This is the second lecture about normals coordinates.

In this lecture we introduce the normal coordinates system.

In this lecture we go further into the study of pseudo-riemannian manifolds.