The Splitting Theorem and topology of noncompact spaces with nonnegative N-Bakry Émery Ricci curvature

Abstract

In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative N N -Bakry Émery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative N N -Bakry Émery Ricci curvature. In addition, we show that if M n M^n is a complete, noncompact Riemannian manifold with nonnegative N N -Bakry Émery Ricci curvature where N > n N>n , then H n − 1 ( M , Z ) H_{n-1}(M,\mathbb {Z}) is 0 0 .