Umbilic points and Real hyperquadrics

1999/02/04 by Won K. Park, Park, Won K.
Mathematics · #32H99 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:32H99

paper · pdf · doi:10.48550/arxiv.math/9902035

arxiv created 1999/02/04 · arxiv updated 2009/11/30

Abstract

We show a refined version of the existence and uniqueness theorem to Chern-Moser normal form. The class of nondegenerate real hypersurfaces in normal form has a natural group action. Umbilic point is defined via normal form. Nondegenerate analytic real hypersurfaces are locally biholomorphic to a real hyperquadric whenever every point is umbilic in this sense.

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