CR structures of codimension 2. (English) Zbl 0675.32017

Let M be a smooth \((2n+k)\)-dimensional manifold. A CR structure of dimension n and codimension k is a pair (D,J), where \(D\subset TM\) is a smooth subbundle of fibre dimension 2n and J is a bundle automorphism of D satisfying: \(J^ 2=-1\) and \(J([X,Y]-[JX,JY])=[JX,Y]+[X,JY]\) for sections X and Y of D.
There are several methods of associating a Cartan connection on a principal bundle to a nondegenerate codimension 1 CR structure. In this paper, the author defines a class of admissible codimension 2 CR structures which is an analogous to the class of nondegenerate CR structures, and for given admissible CR structure on a manifold M he constructs a principal bundle (a subbundle of the frame bundle of M) and a connection on this bundle. Furthermore, he decomposes TM as a direct sum of subbundles of fibre dimensions 1 and 2.
Reviewer: A.Bucki


32V40 Real submanifolds in complex manifolds
32G07 Deformations of special (e.g., CR) structures
32G13 Complex-analytic moduli problems
55R10 Fiber bundles in algebraic topology
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