Critical metrics for quadratic curvature functionals on some solvmanifolds
Critical metrics for quadratic curvature functionals on some solvmanifolds
Abstract We prove the existence of four-dimensional compact manifolds admitting some non-Einstein Lorentzian metrics, which are critical points for all quadratic curvature functionals. For this purpose, we consider left-invariant semi-direct extensions $$G_{\mathcal S}=H \rtimes \exp ({\mathbb {R}}S)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>S</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>H</mml:mi> <mml:mo>⋊</mml:mo> <mml:mo>exp</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> …