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

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.