On pseudo-Hermitian Einstein spaces

Details On pseudo-Hermitian Einstein spaces On pseudo-Hermitian Einstein spaces

2005-02-14

arxiv.org/abs/math/0502287v1

Mathematics

Differential Geometry

16 pages

Scientific paper

We describe and construct here pseudo-Hermitian structures $\theta$ without torsion (i.e. with transversal symmetry) whose Webster-Ricci curvature tensor is a constant multiple of the exterior differential $d\theta$. We call these structures pseudo-Hermitian Einstein and our result states that they all can be derived locally from K{\"a}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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