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arXiv · 2008.05704

Quasi-Einstein shearfree spacetimes lifted from Sasakian manifolds

Masoud Ganji·Gerd Schmalz·Daniel Sykes
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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.

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Masoud Ganji, Gerd Schmalz, Daniel Sykes. 2020-08-13. Quasi-Einstein shearfree spacetimes lifted from Sasakian manifolds. https://arxiv.org/abs/2008.05704

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