Title

Lorentzian Sasaki-Einstein Metrics On Connected Sums Of S² X S³

Document Type

Article

Publication Date

2-1-2011

Published In

Geometriae Dedicata

Abstract

We settle completely an open problem formulated by Boyer and Galicki in [5] which asks whether or not # kS² x S³ are negative Sasakian manifolds for all k. As a consequence of the affirmative answer to this problem, there exists so-called Sasaki eta-Einstein and Lorentzian Sasaki-Einsteinmetrics on these five-manifolds for all k and moreover all of these can be realized as links of isolated hypersurface singularities defined by weighted homogenous polynomials. The key step is to construct infinitely many hypersurfaces in weighted projective space that contain branch divisors Delta = Sigma(i) (1 - 1/m(i)) D-i such that the D-i are rational curves.

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