Abstract
We define and investigate a class of compact homogeneous CR manifolds, that we call \( \mathfrak{n} \)-reductive. They are orbits of minimal dimension of a compact Lie group K 0 in algebraic affine homogeneous spaces of its complexification K. For these manifolds we obtain canonical equivariant fibrations onto complex flag manifolds, generalizing the Hopf fibration \( {S^3}\to \mathbb{C}{{\mathbb{P}}^1} \). These fibrations are not, in general, CR submersions, but satisfy the weaker condition of being CR-deployments; to obtain CR submersions we need to strengthen their CR structure by lifting the complex stucture of the base.
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Altomani, A., Medori, C. & Nacinovich, M. REDUCTIVE COMPACT HOMOGENEOUS CR MANIFOLDS. Transformation Groups 18, 289–328 (2013). https://doi.org/10.1007/s00031-013-9218-9
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DOI: https://doi.org/10.1007/s00031-013-9218-9