3-manifolds with nonnegative Ricci curvature

Abstract

For a noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to ${\mathbb{R}}^3$ or the universal cover splits. As a corollary, it confirms a conjecture of Milnor in dimension 3.

Revised version, accepted by Inventiones Mathematicae

Cited by in corpus (1)

• Splitting theorems, symmetry results and overdetermined problems for Riemannian manifolds