On Strongly Gauduchon Metrics of Compact Complex Manifolds

Jian Xiao*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones (Formula presented.) in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence result of strongly Gauduchon metrics on a compact complex manifold which is fibered over a compact complex curve. In particular, if a compact complex manifold (Formula presented.) has a topologically essential fibration over a compact complex curve, and if the generic fibers satisfy the (Formula presented.)-lemma, then (Formula presented.) admits strongly Gauduchon metrics.

Original languageEnglish (US)
Pages (from-to)2011-2027
Number of pages17
JournalJournal of Geometric Analysis
Volume25
Issue number3
DOIs
StatePublished - Jul 20 2015

Keywords

  • Fibration
  • Positive cones
  • Positive currents
  • Proper modification
  • Strongly Gauduchon metrics

ASJC Scopus subject areas

  • Geometry and Topology

Fingerprint Dive into the research topics of 'On Strongly Gauduchon Metrics of Compact Complex Manifolds'. Together they form a unique fingerprint.

  • Cite this