具有非负Ricci曲率流形的一些拓扑性质  

Some Topological Information of Manifolds with Non-negative Ricci Curvature

作　　者：张易[1] 

机构地区：[1]同济大学数学系,上海200092

出　　处：《大学数学》2016年第2期8-11,共4页College Mathematics

基　　金：国家自然科学基金(11471247)

摘　　要：自从Milnor的基础性论文[5]发表以来,研究非负Ricci曲率的完备非紧流形的拓扑性质就成为一个热门的研究领域,其中代表性的问题为Milnor猜想.Anderson应用体积估计和万有覆盖空间的方法,对此类流形的拓扑性质进行了一定的研究[1-2].本文扩展Anderson的方法,进一步的给出更加一般条件下此类流形的拓扑性质,并对高阶同伦群的研究给出了一些方法.From the fundamental paper of Milnor[5], the research of complete, non-compact and non-negative Ricci curvature is very hot. The representative problem of this field is Milnor＇ s conjecture. By using the methods of volume estimate and universal covering space, Anderson gives some results of topology of these manifolds. In this paper, we generalize the methods of Anderson and give some topological results of these manifolds under some generalized conditions and some methods for researching the higher order homotopy groups.

关 键 词：非负RICCI曲率 拓扑性质 体积估计 

分 类 号：O186.12[理学—数学]