Journal
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
Volume 153, Issue 4, Pages 1272-1296Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/prm.2022.44
Keywords
Quadratic curvature functional; Lorentzian; critical metric; curvature homogeneous; homogeneous; Ricci soliton
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We investigate three-dimensional homogeneous and 1-curvature homogeneous Lorentzian metrics critical to a quadratic curvature functional. We demonstrate that any quadratic curvature functional can have distinct non-Einstein homogeneous critical metrics and that there are homogeneous metrics critical to all quadratic curvature functionals without being Einstein.
We determine all three-dimensional homogeneous and 1-curvature homogeneous Lorentzian metrics which are critical for a quadratic curvature functional. As a result, we show that any quadratic curvature functional admits different non-Einstein homogeneous critical metrics and that there exist homogeneous metrics which are critical for all quadratic curvature functionals without being Einstein.
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