Isotropic quasi-Einstein manifolds
Differential Geometry
2020-01-08 v1 Mathematical Physics
math.MP
Abstract
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 potential function preserves this harmonicity then, in the isotropic case, the manifold is necessarily a -wave. Using the quasi-Einstein equation, further conclusions are obtained for -waves.
Cite
@article{arxiv.1905.03509,
title = {Isotropic quasi-Einstein manifolds},
author = {Miguel Brozos-Vázquez and Eduardo García-Río and Xabier Valle-Regueiro},
journal= {arXiv preprint arXiv:1905.03509},
year = {2020}
}