Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15

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dc.creatorBoyer, Charles P.
dc.creatorGalicki, Krzysztof
dc.creatorKollár, János
dc.creatorThomas, Evan
dc.date2003-11-17
dc.date.accessioned2026-07-07T06:22:07Z
dc.date.available2026-07-07T06:22:07Z
dc.descriptionIn a recent article the first three authors proved that in dimension $4m+1$ all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curvature which, in fact, are Sasakian-Einstein. They also conjectured that all such homotopy spheres in dimension $4m-1, m\geq2$ admit Sasakian-Einstein metrics \cite{BGK}, and proved this for the simplest case, namely dimension $7.$ In this paper we describe computer programs that show that this conjecture is also true for 11-spheres and 15-spheres. Moreover, a program is given that determines the partition of the 8610 deformation classes of Sasakian-Einstein metrics into the 28 distinct oriented diffomorphism types in dimension $7.$
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math/0311293
dc.identifierhttp://arxiv.org/abs/math/0311293
dc.identifierExperimental Mathematics 14 (2005), 61-66.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95816
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subject53C20, 53C12, 14E30
dc.titleEinstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15
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