Abstract
We establish a relation between strict ℂ-convexity of a real hypersurface of ℂn and the behavior of its complex Gauss map. In that way we recover—with an improvement on the regularity—the known results about the topology of these hypersurfaces by using elementary differential geometric arguments. Our approach can be though of as being a complex analog of the description of strictly convex hypersurfaces in Euclidean space via Morse functions associated to pencils of hyperplanes.
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