Lorentzian Sasaki-Einstein Metrics On Connected Sums Of S² X S³
We settle completely an open problem formulated by Boyer and Galicki in  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.
Ralph R. Gomez.
"Lorentzian Sasaki-Einstein Metrics On Connected Sums Of S² X S³".
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