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<p>Inspired by the recent paper of Baltazar and Queiroz (J Geom Anal 34:158, 2024. <a href="https://doi.org/10.1007/s12220-024-01603-y">https://doi.org/10.1007/s12220-024-01603-y</a>), in this article, we prove the rigidity for compact gradient Einstein-type manifolds with nonempty boundary and constant scalar curvature under a pinching condition, which is independent on the potential function. As a special case of gradient Einstein-type manifold, we also give a rigidity result of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11005_2025_1945_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\((m,\rho )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo>,</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-quasi-Einstein manifold with boundary.</p>

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A rigidity condition for compact gradient Einstein-type manifolds with boundary

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Xiaomin Chen

摘要

Inspired by the recent paper of Baltazar and Queiroz (J Geom Anal 34:158, 2024. https://doi.org/10.1007/s12220-024-01603-y), in this article, we prove the rigidity for compact gradient Einstein-type manifolds with nonempty boundary and constant scalar curvature under a pinching condition, which is independent on the potential function. As a special case of gradient Einstein-type manifold, we also give a rigidity result of \((m,\rho )\) ( m , ρ ) -quasi-Einstein manifold with boundary.