Osaka Journal of Mathematics

Compact homogeneous locally conformally Kähler manifolds

Keizo Hasegawa and Yoshinobu Kamishima

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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.

Article information

Osaka J. Math., Volume 53, Number 3 (2016), 683-703.

First available in Project Euclid: 5 August 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32M10: Homogeneous complex manifolds [See also 14M17, 57T15] 53A30: Conformal differential geometry
Secondary: 53B35: Hermitian and Kählerian structures [See also 32Cxx]


Hasegawa, Keizo; Kamishima, Yoshinobu. Compact homogeneous locally conformally Kähler manifolds. Osaka J. Math. 53 (2016), no. 3, 683--703.

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