On the Geometry of Sasakian-Einstein 5-Manifolds

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dc.creatorBoyer, Charles P.
dc.creatorGalicki, Krzysztof
dc.creatorNakamaye, Michael
dc.date2000-12-07
dc.date2001-04-07
dc.date.accessioned2026-07-07T04:39:05Z
dc.date.available2026-07-07T04:39:05Z
dc.descriptionOn 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 Kollár [DK] and Johnson and Kollár [JK1] who give methods for constructing Kähler-Einstein metrics on log del Pezzo surfaces. By [BG1] circle V-bundles over log del Pezzo surfaces with Kähler-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 $\scriptstyle{S^5#l(S^2\times S^3)}.$ More precisely, using methods from Mori theory in algebraic geometry we prove the existence of 14 inequivalent Sasakian-Einstein structures on $\scriptstyle{S^2\times S^3}$ and infinite families of such structures on $\scriptstyle{#l(S^2\times S^3)}$ with $\scriptstyle{2\leq l\leq7}$. We also discuss the moduli problem for these Sasakian-Einstein structures.
dc.description34 pages
dc.identifierhttps://arxiv.org/abs/math/0012047
dc.identifierhttp://arxiv.org/abs/math/0012047
dc.identifierMath. Ann. 325 (2003), 485-524.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60522
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subject53C25 14E30
dc.titleOn the Geometry of Sasakian-Einstein 5-Manifolds
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