Quasi-Einstein shearfree spacetimes lifted from Sasakian manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866910475668684800 |
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| author | Ganji, Masoud Schmalz, Gerd Sykes, Daniel |
| author_facet | Ganji, Masoud Schmalz, Gerd Sykes, Daniel |
| contents | 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 Kähler-Einstein manifold with non-zero Einstein constant has a lift to a shearfree Einstein metric of Petrov type II or D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_05704 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Quasi-Einstein shearfree spacetimes lifted from Sasakian manifolds Ganji, Masoud Schmalz, Gerd Sykes, Daniel Differential Geometry Complex Variables 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 Kähler-Einstein manifold with non-zero Einstein constant has a lift to a shearfree Einstein metric of Petrov type II or D. |
| title | Quasi-Einstein shearfree spacetimes lifted from Sasakian manifolds |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2008.05704 |