Non-K\"ahler Calabi-Yau manifolds

By Valentino Tosatti. 2014

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/043639cbdedee39bc04a5841b479e1c79f18ccfb