Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds

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dc.creatorFutaki, Akito
dc.creatorOno, Hajime
dc.creatorWang, Guofang
dc.date2006-07-24
dc.date2007-01-10
dc.date.accessioned2026-07-07T07:39:25Z
dc.date.available2026-07-07T07:39:25Z
dc.descriptionIn this paper we study compact Sasaki manifolds in view of transverse Kähler geometry and extend some results in Kähler geometry to Sasaki manifolds. In particular we define integral invariants which obstruct the existence of transverse Kähler metric with harmonic Chern forms. The integral invariant $f_1$ for the first Chern class case becomes an obstruction to the existence of transverse Kähler metric of constant scalar curvature. We prove the existence of transverse Kähler-Ricci solitons (or {\it Sasaki-Ricci soliton}) on compact toric Sasaki manifolds whose basic first Chern form of the normal bundle of the Reeb foliation is positive and the first Chern class of the contact bundle is trivial. We will further show that if $S$ is a compact toric Sasaki manifold with the above assumption then by deforming the Reeb field we get a Sasaki-Einstein structure on $S$. As an application we obtain irregular toric Sasaki-Einstein metrics on the unit circle bundles of the powers of the canonical bundle of the two-point blow-up of the complex projective plane.
dc.descriptionThe statement of the results are modified and Proposition 4.3 is added
dc.identifierhttps://arxiv.org/abs/math/0607586
dc.identifierhttp://arxiv.org/abs/math/0607586
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121443
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subject53C55, 53C21, 55N9
dc.titleTransverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
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