Geodesic
Fibrations and globalizations of compact homogeneous CR-manifolds
Izvestiya. Mathematics , Tome 73 (2009) no. 3, pp. 501-553

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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. 
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     author = {B. Gilligan and A. T. Huckleberry},
     title = {Fibrations and globalizations of compact homogeneous {CR-manifolds}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_3_a3/}
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B. Gilligan; A. T. Huckleberry. Fibrations and globalizations of compact homogeneous CR-manifolds. Izvestiya. Mathematics , Tome 73 (2009) no. 3, pp. 501-553. http://geodesic.mathdoc.fr/item/IM2_2009_73_3_a3/