On transversally symmetric pseudo-Einstein and Fefferman-Einstein spaces

摘要

We describe and construct pseudo-Hermitian structures theta without torsion (i.e. with transverse symmetry) whose Webster-Ricci curvature tensor is a constant multiple of the exterior differential d theta. We call these structures TS -pseudo -Einstein and our first result states that all these structures can locally be derived from Kahler-Einstein metrics. Then we discuss the corresponding Fefferman metrics of the TS-pseudo-Einstein structures. These are never Einstein. However, our second result states that they are locally always conformally Einstein.