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- W2950274976 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 three-brane 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 $scriptstyle{S^5#l(S^2times S^3)}.$ More precisely, using methods from Mori theory in algebraic geometry we prove the existence of 14 inequivalent Sasakian-Einstein structures on $scriptstyle{S^2times S^3}$ and infinite families of such structures on $scriptstyle{#l(S^2times S^3)}$ with $scriptstyle{2leq lleq7}$. We also discuss the moduli problem for these Sasakian-Einstein structures." @default.
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- W2950274976 date "2000-12-07" @default.
- W2950274976 modified "2023-09-27" @default.
- W2950274976 title "On the Geometry of Sasakian-Einstein 5-Manifolds" @default.
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