非负Ricci曲率开流形的拓扑

摘要

In this paper, we prove that a complete n-dimensional Riemannian manifold with nonnegative Ricci curvature, large volume growth and injectivity radius bounded from below is diffeomorphic to Rn provided that (Vol[B(p,r)])/(ωnrn)-αM＜(C)/(rn-2+(1)/(n)), for some constant C＞0. We also prove that a complete n-dimensional Riemannian manifold with nonnegative radial curvature Kminp and under some pinched conditions is diffeomorphic to Rn.%我们证明了对于具有非负Ricci曲率,大体积增长且内半径下有界的完备n维Riemann流形,只要存在常数C＞0使得(Vol[B(p,r)])/(ωnrn)-αM＜(C)/(rn-2+(1)/(n)),则它微分同胚于欧式空间Rn. 我们还证明了在某些pinching条件下具有非负射线曲率的完备n维Riemann流形微分同胚与Rn, 改进了已知的结果.