Characterizations Of The Topological Type Of A Class Of Manifolds And The Curvature Of Minimal Submanifolds

In this thesis,we manily study complete noncompact Riemalmian manifolds with Ricci curvature bounded from below and some results of minimal submanifolds.Firstly,in chapter 1,we will make a general description on the recent researches in our field,and give a survey of the researching history about minimal submauifolds.Secondly, in chapter 2,we will give the contents of the relevant preparatory knowledge,which makes a foundation for the proof of the following theorems.Then in chapter 3,it has been proved that under the certain curvature condition or conjugate radius condition,as long as the manifold satisfies the certain condition of the large volume growth,it has finite topological type.At last,in chapter 4,we will give the definition of k-th supreme Ricci curvature and make a portray of a kind of minimal submanifolds' Ricci curvature on this basis.