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Almost CR structures, \(f\)-structures, almost product structures and associated connections. (English) Zbl 0806.53030
Let \(CTM\) be the complexification of the tangent bundle \(TM\) of the manifold \(M\). An almost CR-structure is a complex subbundle \(H \subset CTM\) such that \(H \cap \overline{H} = 0\). In [Geometry of CR- submanifolds, Dordrecht, D. Reidel Publ. Comp. (1986; Zbl 0605.53001)] A. Bejancu gave some relations between \(f\)-structures and almost CR-structures. Annihilating forms and frames defined in the present paper are used to define two higher-codimensional analogues of pseudo-hermitian structures and several examples are given. The notion of partial connection is introduced here to study affine connections associated to almost product structures. The main result states that a nondegenerate annihilating frame for a partially integrable almost CR-structure determines an affine connection. A simple nondegenerate annihilating form determines a pair of partial connections.
Reviewer: C.Tiba (Iaşi)

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
32V40 Real submanifolds in complex manifolds
Citations:
Zbl 0605.53001
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References:
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