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<p>In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition. Moreover, we provide a condition on the norm of the gradient of the potential function in order to classify such structures.</p>

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Compact Einstein-type manifolds with parallel Ricci tensor

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Maria Andrade,
  • Halyson Baltazar,
  • Christopher Queiroz

摘要

In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition. Moreover, we provide a condition on the norm of the gradient of the potential function in order to classify such structures.