Non-Kähler Calabi-Yau manifolds

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.

18 pages; corrected small typos; final version to appear in Contemp. Math

References in corpus (2)

• Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton
• Cocalibrated G_2-manifolds with Ricci flat characteristic connection

Cited by in corpus (19)

• KAWA lecture notes on the Kähler-Ricci flow
• A Construction of Non-Kähler Calabi-Yau Manifolds and New Solutions to the Strominger System
• Inoue surfaces and the Chern-Ricci flow
• Remarks on Chern-Einstein Hermitian metrics
• On the Alesker-Verbitsky conjecture on hyperKähler manifolds
• The prescribed Chern scalar curvature problem
• On cohomogeneity one Hermitian non-Kähler metrics
• On the canonical bundle of complex solvmanifolds and applications to hypercomplex geometry
• Ricci Curvatures on Hermitian manifolds
• Twisted holomorphic symplectic forms
• Hermitian manifolds with semi-positive holomorphic sectional curvature
• Big vector bundles and compact complex manifolds with semi-positive tangent bundles
• Higher dimensional generalizations of twistor spaces
• On some applications of Gauduchon metrics
• Fujiki class $\mathcal{C}$ and holomorphic geometric structures
• $T^4$ fibrations over Calabi-Yau two-folds and non-Kahler manifolds in string theory
• Some computations on trivial canonical-bundle solvmanifolds
• Holomorphic GL(2)-geometry on compact complex manifolds
• Hermitian ranks of compact complex manifolds