Sasakian-Einstein structures on 9#(S-2 x S-3)

摘要

We show that 9#(S(2)xS(3)) admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the first known Einstein metrics on this 5-manifold. In particular, the bound b(2) (M) less than or equal to 8 which holds for any regular Sasakian-Einstein M does not apply to the non-regular case. We also discuss the failure of the Hitchin-Thorpe inequality in the case of 4-orbifolds and describe the orbifold version. [References: 25]