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CR structures on real hypersurfaces of a complex space form. (English) Zbl 0929.53029
A complex space form is a complex \(n\)-dimensional Kählerian manifold of constant holomorphic sectional curvature; if it is complete and simply connected, it is a complex projective space, Euclidean space or hyperbolic space, according to the sign of curvature.
Given a real \(C^\infty\) oriented hypersurface of a complex space form, the author defines a generalized Tanaka connection on it. If the space operator (the Weingarten map) is assumed to be parallel for this connection, the main theorem states that the hypersurface is locally congruent to a hypersurface in a list of cases including some tubes, horospheres, and spherical cylinders.

53C40 Global submanifolds
32V40 Real submanifolds in complex manifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)