This article is cited in 6 papers

Fibrations and globalizations of compact homogeneous CR-manifolds

B. Gilligan^a, A. T. Huckleberry<sup>b

a</sup> University of Regina, Canada
^b Ruhr-Universität Bochum, Mathematischer Institut, Germany

Abstract: Fibration methods which were previously used for complex homogeneous spaces and CR-homogeneous spaces of special types [1]–[4] are developed in a general framework. These include the $\mathfrak g$-anticanonical fibration in the CR-setting, which reduces certain considerations to the compact projective algebraic case, where a Borel–Remmert type splitting theorem is proved. This leads to a reduction to spaces homogeneous under actions of compact Lie groups. General globalization theorems are proved which enable one to regard a homogeneous CR-manifold as an orbit of a real Lie group in a complex homogeneous space of a complex Lie group. In the special case of CR-codimension at most two, precise classification results are proved and are applied to show that in most cases there exists such a globalization.

Keywords: complex homogeneous spaces, homogeneous CR-spaces, homogeneous bundles, globalization.

UDC: 517.55

MSC: 22E15, 32V05, 32V40, 32M10, 53C30, 57S25

Received: 08.10.2007

DOI: 10.4213/im2734

 English version: Izvestiya: Mathematics, 2009, 73:3, 501–553

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