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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.11111 |
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| _version_ | 1866918092757532672 |
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| author | Yin, Hanzhang Zhou, Bin |
| author_facet | Yin, Hanzhang Zhou, Bin |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A topological rigidity theorem on noncompact Hessian manifolds Yin, Hanzhang Zhou, Bin Differential Geometry 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}. |
| title | A topological rigidity theorem on noncompact Hessian manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.11111 |