RIGIDITY AND SPHERE THEOREM FOR MANIFOLDS WITH POSITIVE RICCI CURVATURE

Let M be a complete Riemannian manifold with Ricci curvature having a positive lower bound. In this paper, we prove some rigidity theorems f or M by the existence of a nice minimal hypersurface and a sphere theo rem about M. We also generalize a Myers theorem stating that there is no closed immersed minimal submanifolds in an open hemisphere to the c ase that the ambient space is a complete Riemannian manifold with k-th Ricci curvature having a positive lower bound.