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Cartan connections and CR structures with non-degenerate Levi-form. (English) Zbl 0596.53031
Élie Cartan et les mathématiques d’aujourd’hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Astérisque, No.Hors Sér. 1985, 273-288 (1985).
[For the entire collection see Zbl 0573.00010.]
Let M be a differentiable manifold and G/H be a homogeneous space. A pre- generalized space structure on M is obtained by a certain attaching of G/H to each point of M. In this way a principal bundle E over M with structure group H is constructed. When a Cartan connection on E is chosen we say that M is endowed with a generalized space structure of É. Cartan. In the present paper, the author shows that some of the results obtained up to now on CR-structures follow from a study of CR-structures by means of generalized spaces. By this method he also obtains more information on the geometry of CR-structures.
Reviewer: A.Bejancu

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
32G07 Deformations of special (e.g., CR) structures