| In this thesis,we mainly study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. We study the topology of these manifolds via comparisonal geometry methods.In chapter 1 ,we will make a general description on the recent researches in our field.In chapter 2,we study complete noncompact Riemannian manifolds with nonegative Ricci curvature.We prove that an n-dimensional complete open Riemannian manifold M with Ricci curvature Ric_M ≥ 0 is diffeomorphic to an Euclidean n-space if M satisfies some volume growth conditions.In chapter 3,we prove that a complete noncompact n-dimensional Riemannian manifold M whose Ricci curvature Ric_M ≥(n- 1) has finite topological type or diffeomorphic to R~n if it's Excess function has some upper bound at a point. |
