Study of Riemannian Geometry

Abstract

In this reading project, I have focus on two main theorems of Riemannian geometry, namely Cartan and Rauch theorems. These two theorems provide us two compare the geometrical properties of a given Riemannian manifold with the other one. I started with studying all the tools that are necessary for understanding these theorems. I thoroughly studied Riemannian manifolds, geodesics, connections, curvature and the most interesting Jacobi fields.