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Bach-flat critical metrics for quadratic curvature functionals

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Abstract

In this paper, we study the critical metrics for quadratic curvature functionals involving the Ricci curvature and scalar curvature in the space of Riemannian metrics with unit volume. For these functionals, Einstein metrics are always critical metrics. However, a converse problem is not always true. The purpose of this paper is to show that, under the condition that the critical metrics are Bach-flat, a partial converse is true.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Weimin Sheng & Lisheng Wang

Authors
  1. Weimin Sheng
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  2. Lisheng Wang
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Correspondence to Weimin Sheng.

Additional information

The authors were supported by NSFC 11571304.

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Sheng, W., Wang, L. Bach-flat critical metrics for quadratic curvature functionals. Ann Glob Anal Geom 54, 365–375 (2018). https://doi.org/10.1007/s10455-018-9606-4

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  • DOI: https://doi.org/10.1007/s10455-018-9606-4

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