Obstructions to the existence of Kähler structures on compact complex manifolds

DOI10.1090/S0002-9939-2014-12128-9zbMath1310.32023MaRDI QIDQ3190338

Ionuţ Chiose

Publication date: 16 September 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Fujiki classKähler classSKT metric

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Compact Kähler manifolds: generalizations, classification (32J27)

Related Items

Locally conformal Hermitian metrics on complex non-Kähler manifolds ⋮ On the volume of a pseudo-effective class and semi-positive properties of the Harder–Narasimhan filtration on a compact Hermitian manifold ⋮ A construction of non-Kähler Calabi-Yau manifolds and new solutions to the Strominger system ⋮ Product of generalized \(p\)-Kähler manifolds ⋮ Balanced Hermitian structures on almost abelian Lie algebras ⋮ The complex Monge-Ampère type equation on compact Hermitian manifolds and applications ⋮ Holomorphic deformations of balanced Calabi-Yau $\partial \bar{\partial}$-manifolds ⋮ On the Gauduchon curvature of Hermitian manifolds ⋮ Plurisigned hermitian metrics ⋮ Special Hermitian metrics on Oeljeklaus–Toma manifolds ⋮ A variational approach to SKT and balanced metrics ⋮ Complex analysis -- differential and algebraic methods in Kähler spaces. Abstracts from the workshop held April 9--14, 2023 ⋮ Remarks on astheno-Kähler manifolds, Bott-Chern and Aeppli cohomology groups ⋮ Ricci curvatures on Hermitian manifolds ⋮ On non-Kähler compact complex manifolds with balanced and astheno-Kähler metrics ⋮ On the existence of balanced and SKT metrics on nilmanifolds ⋮ Balanced manifolds and SKT metrics ⋮ Special Hermitian metrics on compact solvmanifolds ⋮ The Kähler rank of compact complex manifolds

Cites Work

• An example of a non-Kählerian complex-analytic deformation of Kählerian complex structures
• An intrinsic characterization of Kähler manifolds
• Algebraicity criteria for compact complex manifolds
• Kähler spaces and proper open morphisms
• On automorphism groups of compact Kähler manifolds
• Courants kählériens et surfaces compactes. (Kähler currents and compact surfaces)
• Transforms of currents by modifications and 1-convex manifolds
• Numerical characterization of the Kähler cone of a compact Kähler manifold
• Compact complex threefolds which are Kähler outside a smooth rational curve
• Unnamed Item