  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.
