Sasakian-Einstein Structures on $9#(S^2\times S^3)$
arXiv:math/0102181
Abstract
We show that $\scriptstyle{#9(S^2\times S^3)}$ 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 which holds for any regular Sasakian-Einstein 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.
14 pages