Locally conformally Kaehler structures on homogeneous spaces
Differential Geometry
2016-01-19 v9 Complex Variables
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.
Keywords
Cite
@article{arxiv.1101.3693,
title = {Locally conformally Kaehler structures on homogeneous spaces},
author = {Keizo Hasegawa and Yoshinobu Kamishima},
journal= {arXiv preprint arXiv:1101.3693},
year = {2016}
}
Comments
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