具有渐近非负Ricci曲率和无穷远处二次曲率衰减的流形  

The Manifolds With Asymptotically Nonnegative Ricci Curvature and Quadratic Curvature Decaying at Infinity

作　　者：张易 

机构地区：[1]同济大学数学科学学院,上海200092

出　　处：《数学进展》2017年第6期945-951,共7页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11201370;No.11571277);陕西省青年科技新星项目(No.2014KJXX-61);陕西省自然科学基金(No.2014JM1007;No.2013JM1017)

摘　　要：本文首先给出了具有渐近非负Ricci曲率流形的体积比较定理.然后给出了流形在一定的曲率衰减的条件下为有限拓扑型的引理,最后利用Abresch-Gromoll估计,给出了具有渐近非负Ricci曲率和无穷远处二次曲率衰减的流形的有限拓扑型条件.In the paper, we give a volume comparison theorem of manifolds with asymp- totically nonnegative Ricci curvature. Then under the condition of quadratic curvature decay- ing at infinity, we give a lemma about finite topological type. Combining these results with Abresch-Gromoll estimates, we get a condition of finite topological type about manifolds with asymptotically nonnegative Ricci curvature and quadratic curvature decaying at infinity.

关 键 词：有限拓扑型 渐近非负Ricci曲率 二次曲率衰减 体积比较 Abresch.Gromoll估计 

分 类 号：O186.12[理学—数学]