Non-K\"ahler Calabi-Yau manifolds
Differential Geometry
2015-11-26 v4 Algebraic Geometry
Complex Variables
Abstract
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-Kahler Calabi-Yau manifolds, and discuss the problem of defining and constructing canonical metrics on them.
Keywords
Cite
@article{arxiv.1401.4797,
title = {Non-K\"ahler Calabi-Yau manifolds},
author = {Valentino Tosatti},
journal= {arXiv preprint arXiv:1401.4797},
year = {2015}
}
Comments
18 pages; corrected small typos; final version to appear in Contemp. Math