Compact Homogeneous Locally Conformally Kaehler Manifolds
Complex Variables
2016-01-19 v1 Differential Geometry
Abstract
In this paper we show as main results two structure theorems of a compact homogeneous locally conformally Kaehler (or shortly l.c.K.) manifold, a holomorphic structure theorem asserting that it has a structure of holomorphic principal fiber bundle over a flag manifold with fiber a 1-dimensional complex torus, and a metric structure theorem asserting that it is necessarily of Vaisman type. We also discuss and determine l.c.K. reductive Lie groups and compact locally homogeneous l.c.K. manifolds of reductive Lie groups.
Cite
@article{arxiv.1312.2202,
title = {Compact Homogeneous Locally Conformally Kaehler Manifolds},
author = {Keizo Hasegawa and Yoshinobu Kamishima},
journal= {arXiv preprint arXiv:1312.2202},
year = {2016}
}
Comments
21 pages. This paper is based on the first part of the original paper "Locally Conformally Kaehler Structures on Homogeneous Spaces" (math.arXiv:1101.3693) with partial revision, containing the main theorems