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Mathematics > Differential Geometry

arXiv:2207.11775 (math)
[Submitted on 24 Jul 2022]

Title:Compact gradient Einstein-type manifolds with boundary and constant scalar curvature

Authors:Xiaomin Chen
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Abstract:Inspired by the study of $V$-static manifold about classification, in this article, we apply the recent results obtained by Freitas and Gomes (Compact gradient Einstein-type manifolds with boundary, 2022) to prove the rigidity results for compact gradient Einstein-type manifolds with nonempty boundary and constant scalar curvature under some suitable pinching conditions. As a special case of gradient Einstein-type manifold, we also give a rigidity result of $(m,\rho)$-quasi-Einstein manifold with boundary.
Comments: 15pages
Subjects: Differential Geometry (math.DG)
MSC classes: 53C25, 53C20, 53C21
Cite as: arXiv:2207.11775 [math.DG]
  (or arXiv:2207.11775v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2207.11775

Submission history

From: Xiaomin Chen [view email]
[v1] Sun, 24 Jul 2022 17:01:54 UTC (11 KB)
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