Compact Homogeneous Locally Conformally Kaehler Manifolds

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  • COMPACT HOMOGENEOUS LOCALLY CONFORMALLY KÄHLER MANIFOLDS

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説明

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.

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

収録刊行物

  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 53 (3), 683-703, 2016-07

    Osaka University and Osaka City University, Departments of Mathematics

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