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<p>The aim of this paper is to study compact quasi-Einstein manifolds with boundary satisfying the zero radial Weyl curvature condition. More precisely, we prove that a compact quasi-Einstein manifold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((M^{n},g,f),\)</EquationSource> </InlineEquation> <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n\ge 5,\)</EquationSource> </InlineEquation> with zero radial Weyl curvature is isometric, up to scaling, to either the standard hemisphere <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {S}^{n}_{+},\)</EquationSource> </InlineEquation> or a warped product <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(g=dt^{2}+\psi ^{2}g_{L},\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(f=f(t)\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(g_{L}\)</EquationSource> </InlineEquation> is Einstein with nonnegative Ricci curvature.</p>

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On compact quasi-Einstein metrics with zero radial Weyl curvature

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月29日

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  • H. Baltazar,
  • J. Carvalho,
  • X. Chen

摘要

The aim of this paper is to study compact quasi-Einstein manifolds with boundary satisfying the zero radial Weyl curvature condition. More precisely, we prove that a compact quasi-Einstein manifold \((M^{n},g,f),\) \(n\ge 5,\) with zero radial Weyl curvature is isometric, up to scaling, to either the standard hemisphere \(\mathbb {S}^{n}_{+},\) or a warped product \(g=dt^{2}+\psi ^{2}g_{L},\) and \(f=f(t)\) , where \(g_{L}\) is Einstein with nonnegative Ricci curvature.