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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 3, Pages 67–126 (Mi izv2734)  

This article is cited in 4 scientific papers (total in 4 papers)

Fibrations and globalizations of compact homogeneous CR-manifolds

B. Gilligana, A. T. Huckleberryb

a 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.

DOI: https://doi.org/10.4213/im2734

Full text: PDF file (920 kB)
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English version:
Izvestiya: Mathematics, 2009, 73:3, 501–553

Bibliographic databases:

UDC: 517.55
MSC: 22E15, 32V05, 32V40, 32M10, 53C30, 57S25
Received: 08.10.2007

Citation: B. Gilligan, A. T. Huckleberry, “Fibrations and globalizations of compact homogeneous CR-manifolds”, Izv. RAN. Ser. Mat., 73:3 (2009), 67–126; Izv. Math., 73:3 (2009), 501–553

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gilligan B., Oeljeklaus K., “Compact CR-solvmanifolds as Kähler obstructions”, Math. Z., 269:1-2 (2011), 179–191  crossref  mathscinet  zmath  isi
    2. A. Altomani, C. Medori, M. Nacinovich, “uctive compact homogeneous CR manifolds”, Transform. Groups, 18:2 (2013), 289–328  crossref  mathscinet  zmath  isi
    3. Ahmadi S.R. Gilligan B., “Complexifying Lie Group Actions on Homogeneous Manifolds of Non-Compact Dimension Two”, Can. Math. Bul.-Bul. Can. Math., 57:4 (2014), 673–682  crossref  mathscinet  zmath  isi
    4. Ahmadi R. Gilligan B., “Classification of Kahler Homogeneous Manifolds of Non-Compact Dimension Two”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 17:4 (2017), 1231–1254  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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