Calabi’s Conjecture of the Kähler–Ricci Soliton Type

Kenta Tottori

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we discuss Calabi’s equation of the Kähler–Ricci soliton type on a compact Kähler manifold. This equation was introduced by Zhu as a generalization of Calabi’s conjecture. We give necessary and sufficient conditions for the unique existence of a solution for this equation on a compact Kähler manifold with a holomorphic vector field which has a zero point. We also consider the case of a nowhere vanishing holomorphic vector field, and give sufficient conditions for the unique existence of a solution for this equation.

Original languageEnglish
Pages (from-to)3325-3343
Number of pages19
JournalJournal of Geometric Analysis
Volume26
Issue number4
DOIs
Publication statusPublished - 2016 Oct 1

Keywords

  • Calabi’s conjecture
  • Geometric flow
  • Holomorphic vector field
  • Kähler–Ricci soliton

ASJC Scopus subject areas

  • Geometry and Topology

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