New Einstein Metrics in Dimension Five

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dc.creatorBoyer, Charles P.
dc.creatorGalicki, Krzysztof
dc.date2000-03-27
dc.date2001-09-05
dc.date.accessioned2026-07-07T04:34:28Z
dc.date.available2026-07-07T04:34:28Z
dc.descriptionThe purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on $\scriptstyle{S^2\times S^3}$ and on $\scriptstyle{(S^2\times S^3)# (S^2\times S^3).}$ These give the first known examples of non-regular Sasakian-Einstein 5-manifolds. Our method involves describing the Sasakian-Einstein structures as links of certain isolated hypersurface singularities, and makes use of the recent work of Demailly and Kollár, AG/9910118, who obtained new examples of Kähler-Einstein del Pezzo surfaces with quotient singularities.
dc.descriptionRevised version with minor corrections and udated references, 15 pages, to appear in JDG
dc.identifierhttps://arxiv.org/abs/math/0003174
dc.identifierhttp://arxiv.org/abs/math/0003174
dc.identifierJ. Diff. Geom. 57 (2001) 443-463.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58912
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.subject53C25, 53C12, 14E30
dc.titleNew Einstein Metrics in Dimension Five
dc.typetext

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