A topological rigidity theorem on noncompact Hessian manifolds
Differential Geometry
2025-07-16 v1
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 if its tangent bundle has maximal volume growth. This is an improvement of Theorem 1.3 in Jiao-Yin \cite{JY25}.
Cite
@article{arxiv.2507.11111,
title = {A topological rigidity theorem on noncompact Hessian manifolds},
author = {Hanzhang Yin and Bin Zhou},
journal= {arXiv preprint arXiv:2507.11111},
year = {2025}
}