Classification of non-Kahler surfaces and locally conformally Kahler geometry

Abstract

We give a mostly self-contained proof of the classification of non-Kahler surfaces based on Buchdahl-Lamari theorem. We also prove that all non-Kahler surfaces which are not of class VII are locally conformally Kahler.

39 pages, v. 3.0, references added, misprints corrected, several proofs changed in sections 4 and 5. To appear in Russian Math. Surveys

References in corpus (1)

• Twistors and Bi-Hermitian Surfaces of Non-Kähler Type

Cited by in corpus (4)

• Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds
• Balanced metrics and Gauduchon cone of locally conformally Kahler manifolds
• Holomorphic tensors on Vaisman manifolds
• Do products of compact complex manifolds admit LCK metrics?