Locally conformally Kaehler structures on homogeneous spaces

Details Locally conformally Kaehler structures on homogeneous spaces Locally conformally Kaehler structures on homogeneous spaces

2011-01-19

arxiv.org/abs/1101.3693v8

Mathematics

Differential Geometry

22 pages

Scientific paper

We show as a main result a structure theorem of compact homogeneous locally conformal Kaehler (or shortly l.c.K.) manifolds, asserting that it has a structure of holomorphic fiber bundle over a flag manifold with fiber a 1-dimensional complex torus. We also discuss compact locally homogeneous l.c.K. manifolds; and classify all complex surfaces admitting homogeneous and locally homogeneous l.c.K. structures.

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