Abstract

The main goal of this seminar is to understand the Cheeger-Colding theory on the Gromov-Hausdorff limit, and its applications. In this first talk, we will go through the Cheeger-Gromoll splitting theorem, it states that if a complete Riemannian manifold with non-negative Ricci curvature has a straight line, then the Riemannian manifold is isometric to a product space . Also, we will consider further applications on compact manifolds with non-negative Ricci curvature.