A new holomorphic invariant and uniqueness of Kähler-Ricci solitons

Gang Tian*, Xiaohua Zhu

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    97 Citations (Scopus)

    Abstract

    In this paper, a new holomorphic invariant is defined on a compact Kähler manifold with positive first Chern class and nontrivial holomorphic vector fields. This invariant generalizes the Futaki invariant. We prove that this invariant is an obstruction to the existence of Kähler-Ricci solitons. In particular, using this invariant together with the main result in [TZ1], we solve completely the uniqueness problem of Kähler-Ricci solitons. Two functionals associated to the new holomorphic invariant are also discussed. The main result here was announced in [TZ2].

    Original languageEnglish
    Pages (from-to)297-325
    Number of pages29
    JournalCommentarii Mathematici Helvetici
    Volume77
    Issue number2
    DOIs
    Publication statusPublished - 2002

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