In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain dista...In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain distance functions satisfy a reasonable condition.展开更多
in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1...in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1）/k＋1（1-α/2）}≤for some COllstant ε〉0 We also prove that a conlplete Riemannian manifold with nonnegative kth-Ricci curvature and undler some pinching conditions is diffeomorphic to R^n.展开更多
文摘In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain distance functions satisfy a reasonable condition.
文摘in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1）/k＋1（1-α/2）}≤for some COllstant ε〉0 We also prove that a conlplete Riemannian manifold with nonnegative kth-Ricci curvature and undler some pinching conditions is diffeomorphic to R^n.
