English

Quasi-Einstein shearfree spacetimes lifted from Sasakian manifolds

Differential Geometry 2024-06-10 v5 Complex Variables

Abstract

In this article we prove that a certain class of {\it smooth} Sasakian manifolds admits lifts to 4-dimensional quasi-Einstein shearfree spacetimes of Petrov type II or D. This is related to an analogous result by Hill, Lewandowski and Nurowski \cite{HLN} for general {\it real-analytic} CR manifolds. In particular, this holds for all tubular CR manifolds. Furthermore, we show that any Sasakian manifold with underlying K\"ahler-Einstein manifold with non-zero Einstein constant has a lift to a shearfree Einstein metric of Petrov type II or D.

Keywords

Cite

@article{arxiv.2008.05704,
  title  = {Quasi-Einstein shearfree spacetimes lifted from Sasakian manifolds},
  author = {Masoud Ganji and Gerd Schmalz and Daniel Sykes},
  journal= {arXiv preprint arXiv:2008.05704},
  year   = {2024}
}

Comments

We corrected few typos in theorems 3.2, 4.4 and, example 4.4. We have made some changes in the title of the paper