Holomorphic mappings and the geometry of hypersurfaces. (English. Russian original) Zbl 0781.32013

Several complex analysis. I. Introduction to complex analysis, Encycl. Math. Sci. 7, 159-214 (1990); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 7, 167-226 (1985).
Summary: In the paper, non-degenerate (in the Levy sense), real-analytic hypersurfaces of complex manifolds are considered; questions concerning automorphisms of surfaces and geometry of chains, possibilities of continuation of holomorphic mappings and classification problems are discussed; the normal form of writing-down the surfaces and the normal parametrization of chains are discussed in detail. Some results concerning smooth surfaces are considered, as well.
The bibliography contains 47 references.


32C05 Real-analytic manifolds, real-analytic spaces
32V40 Real submanifolds in complex manifolds
32D15 Continuation of analytic objects in several complex variables