Sasakian-Einstein Structures on $9#(S^2\times S^3)$

Details Sasakian-Einstein Structures on $9#(S^2\times S^3)$ Sasakian-Einstein Structures on $9#(S^2\times S^3)$

2001-02-22

arxiv.org/abs/math/0102181v1

Transactions of the American Mathematical Society 354, 2983-2996 (2002)

Mathematics

Differential Geometry

14 pages

Scientific paper

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 $\scriptstyle{b_2(M)\leq8}$ which holds for any regular Sasakian-Einstein $\scriptstyle{M}$ 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.

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