Mathematics – Differential Geometry
Scientific paper
2000-03-27
J. Diff. Geom. 57 (2001) 443-463.
Mathematics
Differential Geometry
Revised version with minor corrections and udated references, 15 pages, to appear in JDG
Scientific paper
The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on $\scriptstyle{S^2\times S^3}$ and on $\scriptstyle{(S^2\times S^3)# (S^2\times S^3).}$ These give the first known examples of non-regular Sasakian-Einstein 5-manifolds. Our method involves describing the Sasakian-Einstein structures as links of certain isolated hypersurface singularities, and makes use of the recent work of Demailly and Koll\'ar, AG/9910118, who obtained new examples of K\"ahler-Einstein del Pezzo surfaces with quotient singularities.
Boyer Charles P.
Galicki Krzysztof
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