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<p>In this paper, we obtain the existence criteria for a geometric flow on noncompact affine Riemannian manifolds. Our results can be regarded as a real version of Lee and Tam (J Differ Geom 115(3):529–564, 2020). As an application, we prove that a complete noncompact Hessian manifold with nonnegative Hessian sectional curvature and bounded geometry is diffeomorphic to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2024_2904_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> if its tangent bundle has maximal volume growth.</p>

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A geometric flow on noncompact affine Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Heming Jiao,
  • Hanzhang Yin

摘要

In this paper, we obtain the existence criteria for a geometric flow on noncompact affine Riemannian manifolds. Our results can be regarded as a real version of Lee and Tam (J Differ Geom 115(3):529–564, 2020). As an application, we prove that a complete noncompact Hessian manifold with nonnegative Hessian sectional curvature and bounded geometry is diffeomorphic to \(\mathbb {R}^n\) R n if its tangent bundle has maximal volume growth.