#### 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.

#### Recommended Citation

Ralph R. Gomez.
(2011).
"Lorentzian Sasaki-Einstein Metrics On Connected Sums Of S² X S³".
*Geometriae Dedicata*.
Volume 150,
Issue 1.
249-255.

http://works.swarthmore.edu/fac-math-stat/53

## Comments

This work is a preprint available from arXiv.org at arXiv:0906.2215v2.

The final publication version can be freely accessed courtesy of Springer Nature's SharedIt service.