Locally conformally Kähler manifolds. A selection of results

Abstract

I present a selection of results on locally conformally Kähler geometry published after 1997. The proofs are mainly sketched, some of them are even omitted. Several open problems are indicated in the end.

arXiv commentThe notion of rank and presentation (Paragraph 2.2.) added. References updated

References in corpus (4)

• Reduction of Vaisman structures in complex and quaternionic geometry
• Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length
• Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length
• Weyl structures on quaternionic manifolds. A state of the art

Cited by in corpus (7)

• Morse-Novikov cohomology of locally conformally Kähler manifolds
• On pseudo-harmonic maps in conformal geometry
• Fibrations and fundamental groups of Kaehler-Weyl manifolds
• Einstein-Weyl structures on complex manifolds and conformal version of Monge-Ampere equation
• Hard Lefschetz Theorem for Vaisman manifolds
• Biharmonic holomorphic maps and conformally Kahler geometry
• A Moduli Space of the Quaternionic Hopf Surface Encodes Standard Model Physics