A topological rigidity theorem on noncompact Hessian manifolds via geometric flow

In this work, we obtain a short time solution for a geometric flow on noncompact affine Riemannian manifolds. Using this result, we can construct a Hessian metric with nonnegative bounded Hessian sectional curvature on some Hessian manifolds with nonnegative Hessian sectional curvature. Our results can be regarded as a real version of Lee-Tam [1]. As an application, we prove that a complete noncompact Hessian manifold with nonnegative Hessian sectional curvature is diffeomorphic to Rⁿ if its tangent bundle has maximal volume growth. This is an improvement of Theorem 1.3 in Jiao-Yin [2].