A geometric flow on noncompact affine Riemannian manifolds

Abstract

In this paper, we obtain the existence criteria for a geometic flow on noncompact affine Riemannian manifolds. Our results can be regarded as a real version of Lee-Tam [19]. As an application, we prove that a complete noncompact Hessian manifold with nonnegative Hessian sectional curvature and bounded geometry is diffeomorphic to ${\mathbb{R}}^n$ if its tangent bundle has maximal volume growth.

arXiv commentarXiv admin note: text overlap with arXiv:math/0504422, arXiv:1708.00141 by other authors