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Introduction to the geometry of CR-manifolds. (English. Russian original) Zbl 0742.32006

Russ. Math. Surv. 46, No. 1, 95-197 (1991); translation from Usp. Mat. Nauk 46, No. 1(277), 81-164 (1991).
The CR manifolds, i.e. the Cauchy-Riemann manifolds, are of special interest in the theory of complex functions of several complex variables. The aim is to present the general theory of CR-manifolds by underlying their importance in analysis (in the theory of CR-functions) and the geometric aspects of the presented results.
The author’s contribution consists of new proofs, examples and a very clear and detailed presentation.
Contents: Introduction. 1. Classes of CR-manifolds. 2. CR-fields. 3. Annihilating forms. RC-manifolds. 4. The Levi form. 5. CR-foliations. 6. Defining functions. 7. Totally real manifolds. References.

MSC:

32V99 CR manifolds
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