## On the Geometry of Sasakian-Einstein 5-Manifolds (0)

Venue: | MATH. ANN |

Citations: | 33 - 16 self |

### BibTeX

@ARTICLE{Boyer_onthe,

author = {Charles P. Boyer and Krzysztof Galicki and Michael Nakamaye},

title = {On the Geometry of Sasakian-Einstein 5-Manifolds },

journal = {MATH. ANN},

year = {},

volume = {325},

pages = {485--524}

}

### OpenURL

### Abstract

On simply connected five manifolds Sasakian-Einstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for threebrane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kollar [DK] and Johnson and Kollar [JK1] who give methods for constructing Kahler-Einstein metrics on log del Pezzo surfaces. By [BG1] circle V-bundles over log del Pezzo surfaces with Kahler-Einstein metrics have Sasakian-Einstein metrics on the total space of the bundle. Here these simply connected 5-manifolds arise as links of isolated hypersurface singularities which by the well known work of Smale [Sm] together with [BG3] must be diffeomorphic to S 5