The geometry of hyperbolic and elliptic CR-manifolds of codimension two
Gerd Schmalz and Jan Slovak
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Submission date: 27. Jan. 1999
published in: The Asian journal of mathematics, 4 (2000) 3, p. 565-597
DOI number (of the published article): 10.4310/AJM.2000.v4.n3.a5
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The general theory of parabolic geometries is applied to the study of the normal Cartan connections for all hyperbolic and elliptic 6-dimensional CR-manifolds of codimension two. The geometric meaning of the individual components of the torsion is explained and the chains of dimensions one and two are discussed. This seems to be the first application of the general methods to a geometry with a non-connected and non-simple structure group.