On Sasakian-Einstein Geometry

Details On Sasakian-Einstein Geometry On Sasakian-Einstein Geometry

1998-11-16

arxiv.org/abs/math/9811098v2

Int.J.Math. 11 (2000) 873-909

Mathematics

Differential Geometry

31 pages, revised and corrected version

Scientific paper

We discuss Sasakian-Einstein geometry under a quasi-regularity assumption. It is shown that the space of all quasi-regular Sasakian-Einstein orbifolds has a natural multiplication on it. Furthermore, necessary and sufficient conditions are given for the `product' of two Sasakian-Einstein manifolds to be a smooth Sasakian-Einstein manifold. Using spectral sequence arguments we work out the cohomology ring in many cases of interest. This type of geometry has recently become of interest in the physics of supersymmetric conformal field theories.

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