Abstract: 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 ... for some constant ε＞0.We also prove that a complete Riemannian manifold with nonnegative kth-Ricci curvature and under some pinching conditions is diffeomorphic to Rⁿ.

Key words: Excess ,  function;large ,  volume ,  growth;nonnegative ,  kth-Ricci ,  curvature