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On pseudo-Hermitian Einstein spaces

Felipe Leitner
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Abstract

We describe and construct here pseudo-Hermitian structures $θ$ without torsion (i.e. with transversal symmetry) whose Webster-Ricci curvature tensor is a constant multiple of the exterior differential $dθ$. We call these structures pseudo-Hermitian Einstein and our result states that they all can be derived locally from K{ä}hler-Einstein metrics. Moreover, we discuss the corresponding Fefferman metrics of the pseudo-Hermitian Einstein structures. These Fefferman metrics are never Einstein, but they are locally always conformally Einstein.

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Felipe Leitner. 2005-02-14. On pseudo-Hermitian Einstein spaces. https://arxiv.org/abs/math/0502287

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