Umbilic points and Real hyperquadrics
Won K. Park

TL;DR
This paper refines the existence and uniqueness of Chern-Moser normal form for real hypersurfaces, linking umbilic points to hyperquadrics and exploring their symmetry properties.
Contribution
It provides a refined theorem for normal forms and characterizes umbilic points via this form, connecting local biholomorphic equivalence to hyperquadrics.
Findings
Refined existence and uniqueness theorem for Chern-Moser normal form.
Characterization of umbilic points through normal form.
Nondegenerate hypersurfaces are locally biholomorphic to hyperquadrics if all points are umbilic.
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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Taxonomy
TopicsHolomorphic and Operator Theory · Meromorphic and Entire Functions · Analytic and geometric function theory
