A new holomorphic invariant and uniqueness of Kähler-Ricci solitons

Gang Tian, Xiaohua Zhu

Research output: Contribution to journalArticlepeer-review

94 Scopus citations


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 (US)
Pages (from-to)297-325
Number of pages29
JournalCommentarii Mathematici Helvetici
Issue number2
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Holomorphic vector field
  • Kähler-Ricci soliton
  • New holomorphic invariant


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