Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 53, Number 3 (2016), 683-703.
Compact homogeneous locally conformally Kähler manifolds
In this paper we show as main results two structure theorems of a compact homogeneous locally conformally Kähler (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.
Osaka J. Math., Volume 53, Number 3 (2016), 683-703.
First available in Project Euclid: 5 August 2016
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Hasegawa, Keizo; Kamishima, Yoshinobu. Compact homogeneous locally conformally Kähler manifolds. Osaka J. Math. 53 (2016), no. 3, 683--703. https://projecteuclid.org/euclid.ojm/1470413984