Three-dimensional homogeneous critical metrics for quadratic curvature functionals

Abstract

We show the existence of non-Einstein homogeneous critical metrics for any quadratic curvature functional in dimension three.

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Correspondence to E. García-Río.

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Supported by projects MTM2016-75897-P, and ED431C 2019/10 with FEDER Funds (Spain).

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Brozos-Vázquez, M., García-Río, E. & Caeiro-Oliveira, S. Three-dimensional homogeneous critical metrics for quadratic curvature functionals. Annali di Matematica (2020). https://doi.org/10.1007/s10231-020-00999-y

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Keywords

  • Quadratic curvature functional
  • Critical metric
  • Homogeneous space
  • Lie group

Mathematics Subject Classification

  • 53C21
  • 53B20
  • 53C24