Uniqueness and examples of compact toric Sasaki-Einstein metrics

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dc.creatorCho, Koji
dc.creatorFutaki, Akito
dc.creatorOno, Hajime
dc.date2007-01-04
dc.date2007-01-10
dc.date.accessioned2026-07-07T11:03:19Z
dc.date.available2026-07-07T11:03:19Z
dc.descriptionIn [11] it was proved that, given a compact toric Sasaki manifold of positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on $S^5 \sharp k(S^2 \times S^3)$ for each positive integer $k$.
dc.descriptionStatements of the results are modified
dc.identifierhttps://arxiv.org/abs/math/0701122
dc.identifierhttp://arxiv.org/abs/math/0701122
dc.identifierCommun.Math.Phys.277:439-458,2008
dc.identifierdoi:10.1007/s00220-007-0374-4
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/188551
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subject53C55, 53C21, 55N91
dc.titleUniqueness and examples of compact toric Sasaki-Einstein metrics
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