Uniqueness and examples of compact toric Sasaki-Einstein metrics

Koji Cho, Akito Futaki, Hajime Ono

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

In [11] it was proved that, given a compact toric Sasaki manifold with 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 S5 # k(S2 × S3) for each positive integer k.

Original languageEnglish
Pages (from-to)439-458
Number of pages20
JournalCommunications in Mathematical Physics
Volume277
Issue number2
DOIs
Publication statusPublished - Jan 1 2008

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Sasaki Metric
Einstein Metrics
uniqueness
Uniqueness
Chern Classes
bundles
Bundle
Automorphism Group
integers
Modulo
cones
Trivial
Cone
Transverse
Diagram
diagrams
Contact
Imply
Integer

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Uniqueness and examples of compact toric Sasaki-Einstein metrics. / Cho, Koji; Futaki, Akito; Ono, Hajime.

In: Communications in Mathematical Physics, Vol. 277, No. 2, 01.01.2008, p. 439-458.

Research output: Contribution to journalArticle

Cho, Koji ; Futaki, Akito ; Ono, Hajime. / Uniqueness and examples of compact toric Sasaki-Einstein metrics. In: Communications in Mathematical Physics. 2008 ; Vol. 277, No. 2. pp. 439-458.
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