标题： 非紧Hessian流形上的拓扑刚性定理 显示英文标题

标题： A topological rigidity theorem on noncompact Hessian manifolds

摘要： 在本工作中，我们得到了非紧致仿射黎曼流形上几何流的短期解。 利用这个结果，我们可以在某些具有非负Hessian截面曲率的Hessian流形上构造出具有非负有界Hessian截面曲率的Hessian度量。 我们的结果可以被视为Lee-Tam \cite{LT20}的实版本。 作为应用，我们证明了如果其切丛具有最大体积增长，则具有非负Hessian截面曲率的完备非紧Hessian流形微分同胚于 $\mathbb{R}^n$。 这是对Jiao-Yin \cite{JY25}中定理1.3的改进。 显示英文摘要

摘要： 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 \cite{LT20}. As an application, we prove that a complete noncompact Hessian manifold with nonnegative Hessian sectional curvature is diffeomorphic to $\mathbb{R}^n$ if its tangent bundle has maximal volume growth. This is an improvement of Theorem 1.3 in Jiao-Yin \cite{JY25}.