An integral invariant from the view point of locally conformally Kähler geometry

Akito Futaki, Kota Hattori, Liviu Ornea

Research output: Contribution to journalArticle

Abstract

In this article we study an integral invariant which obstructs the existence on a compact complex manifold of a volume form with the determinant of its Ricci form proportional to itself, in particular obstructs the existence of a Kähler-Einstein metric, and has been studied since 1980s. We study this invariant from the view point of locally conformally Kähler geometry. We first see that we can define an integral invariant for coverings of compact complex manifolds with automorphic volume forms. This situation typically occurs for locally conformally Kähler manifolds. Secondly, we see that this invariant coincides with the former one. We also show that the invariant vanishes for any compact Vaisman manifold.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalManuscripta Mathematica
Volume140
Issue number1-2
DOIs
Publication statusPublished - 2013
Externally publishedYes

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Invariant
Compact Manifold
Complex Manifolds
Einstein Metrics
Vanish
Determinant
Covering
Directly proportional
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

An integral invariant from the view point of locally conformally Kähler geometry. / Futaki, Akito; Hattori, Kota; Ornea, Liviu.

In: Manuscripta Mathematica, Vol. 140, No. 1-2, 2013, p. 1-12.

Research output: Contribution to journalArticle

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