A topological rigidity theorem on noncompact Hessian manifolds

Hanzhang Yin; Bin Zhou

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arXiv · 2507.11111

A topological rigidity theorem on noncompact Hessian manifolds

Hanzhang Yin·Bin Zhou

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Abstract

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}.

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Hanzhang Yin, Bin Zhou. 2025-07-15. A topological rigidity theorem on noncompact Hessian manifolds. https://arxiv.org/abs/2507.11111

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