Uniqueness and examples of compact toric Sasaki-Einstein metrics

Koji Cho, Akito Futaki, Hajime Ono

    Research output: Contribution to journalArticlepeer-review

    42 Citations (Scopus)


    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
    Issue number2
    Publication statusPublished - Jan 2008

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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