1999/04/13 by Dmitry V. Alekseevsky, Alekseevsky, Dmitry V., Andrea F. Spiro +1
Mathematics · #32C16 (Primary) #53C15 (Secondary) #53C30 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG #msc:32C16 #msc:53C15 #msc:53C30
paper · pdf · doi:10.48550/arxiv.math/9904054
In this new version, there are no structural changes from the previous. Some mistakes in the tables of Theorem 1.4, of Theorem 1.5 and of Definition 1.7 have been corrected
arxiv created 2000/12/12 · arxiv updated 2009/11/30
An explicit classification of simply connected compact homogeneous CR manifolds G/L of codimension one, with non-degenerate Levi form, is given. There are three classes of such manifolds: a) the standard CR homogeneous manifolds which are homogeneous S1-bundles over a flag manifold F, with CR structure induced by an invariant complex structure on F; b) the Morimoto-Nagano spaces, i.e. sphere bundles S(N)⊂ TN of a compact rank one symmetric space N = G/H, with the CR structure induced by the natural complex structure of TN = G^\C/H^\C; c) the following manifolds: SUn/T1⋅ SUn-2, SUp× SUq/T1 ⋅ Up-2⋅ Uq-2, SUn/T1⋅ SU2⋅ SU2⋅ SUn-4, SO10/T1⋅ SO6, E6/T1⋅ SO8; these manifolds admit canonical holomorphic fibrations over a flag manifold (F,JF) with typical fiber S(Sk), where k = 2, 3, 5, 7 or 9, respectively; the CR structure is determined by the invariant complex structure JF on F and by an invariant CR structure on the typical fiber, depending on one complex parameter.