  In this paper, we study the topology of complete noncompact Riemannian
manifolds with asymptotically nonnegative Ricci curvature. We show that a
complete noncompact manifold with asymptoticaly nonnegative Ricci curvature and
sectional curvature decay at most quadratically is diffeomorphic to a Euclidean
n-space R^n under some conditions on the density of rays starting from the base
point p or on the volume growth of geodesic balls in M.
