Uniqueness and examples of compact toric Sasaki-Einstein metrics

Koji Cho, Akito Futaki, Hajime Ono

研究成果: Contribution to journalArticle査読

39 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)439-458
ページ数20
ジャーナルCommunications in Mathematical Physics
277
2
DOI
出版ステータス出版済み - 1 2008

All Science Journal Classification (ASJC) codes

  • 統計物理学および非線形物理学
  • 数理物理学

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