arXiv subjects
Publications and source records attributed to Ramon Vazquez-Lorenzo.
We describe four-dimensional Lorentzian algebraic Ricci solitons. In sharp contrast with the Riemannian situation, any connected and simply connected four-dimensional Lie group admits a left-invariant Lorentz metric which is a Ricci soliton.
We describe all Lorentzian semi-direct extensions of the Heisenberg group which are conformally Einstein. As a by side result, Bach-flat left-invariant Lorentzian metrics on semi-direct extensions of the Heisenberg group are classified, thus providing new background solutions in conformal gravity.
A complete description of Osserman four-manifolds whose Jacobi operators have a nonzero double root of the minimal polynomial is given.