Non-Kähler calabi-yau manifolds

Valentino Tosatti

Research output: Chapter in Book/Report/Conference proceedingChapter


We study the class of compact complex manifolds whose first Chern class vanishes in the Bott-Chern cohomology. This class includes all manifolds with torsion canonical bundle, but it is strictly larger. After making some elementary remarks, we show that a manifold in Fujiki’s class C with vanishing first Bott-Chern class has torsion canonical bundle. We also give some examples of non-Kähler Calabi-Yau manifolds, and discuss the problem of defining and constructing canonical metrics on them.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages17
StatePublished - 2015

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


  • Calabi-Yau manifolds
  • Canonical bundle
  • Non-Kähler manifolds

ASJC Scopus subject areas

  • General Mathematics


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