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Ricci solitons on four-dimensional Lorentzian Lie groups
We determine all non-Einstein Ricci solitons on four-dimensional Lorentzian Lie groups whose soliton vector field is left-invariant. In addition to pp-wave and plane wave Lie groups, there are four families of Lorentzian ...
Homogeneous generalized Einstein manifolds in dimension four
We classify homogeneous four-dimensional manifolds satisfying a curvature condition which naturally generalizes the Einstein one. Our work leads to new examples of self-similar solutions of the two-loop renormalization group flow
Homogeneous and curvature homogeneous Lorentzian critical metrics
(Cambridge University Press, 2022)
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 ...