Compact Homogeneous Locally Conformally Kaehler Manifolds

Autor:	Hasegawa, Keizo, Kamishima, Yoshinobu
Rok vydání:	2013
Předmět:	Mathematics - Complex Variables Mathematics - Differential Geometry
Zdroj:	Osaka Journal of Mathematics, Vol. 53, No. 3 (2016)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1312.2202 Zobrazit plný text záznamu View this record from Arxiv