49 citations · 183 across the 35 of their papers we have counts for
36 papers
Four-dimensional Lorentzian algebraic Ricci solitons
Eduardo Garcia-Rio, Rosalia Rodriguez-Gigirey, 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 adm…
Conformally Einstein Lorentzian Lie groups with Heisenberg symmetry
Esteban Calviño-Louzao, Eduardo Garcia-Rio, Ixchel Gutierrez-Rodriguez +1
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-d…
Isotropic quasi-Einstein manifolds
Miguel Brozos-Vázquez, Eduardo García-Río, Xabier Valle-Regueiro
We investigate the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor. We show that if the Weyl tensor is harmonic and the…
Constructing Bach Flat Manifolds of signature using the modified Riemannian extension
E. Calviño-Louzao, E. García-Río, P. Gilkey +2
We use the modified Riemannian extension of an affine surface to construct Bach flat manifolds. As all these examples are VSI (vanishing scalar invariants), we shall construct scal…
Affine surfaces which are Kähler, para-Kähler, or nilpotent Kähler
E. Calviño-Louzao, E. García-Río, P. Gilkey +2
Motivated by the construction of Bach flat neutral signature Riemannian extensions, we study the space of parallel trace free tensors of type on an affine surface. It is sh…
Bach-flat isotropic gradient Ricci solitons
Esteban Calviño-Louzao, Eduardo García-Río, Ixchel Gutiérrez-Rodríguez +1
We construct examples of Bach-flat gradient Ricci solitons which are neither half conformally flat nor conformally Einstein.