Locally conformally Kaehler structures on homogeneous spaces

Abstract

We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey of known results along with some new results and observations; in particular we make a complete classification of 4-dimensional homogeneous and locally homogeneous l.c.K. manifolds in terms of Lie algebras.

26 pages. The original paper has been separated into two papers; this paper and another paper {arXiv:1312.2202] which contains the detailed proof of Theorem 1. To appear in Memorial Volume of Professor Shoshichi Kobayashi, Progress in Mathematics, Springer