# Umbilic points and Real hyperquadrics

@article{Park1999UmbilicPA, title={Umbilic points and Real hyperquadrics}, author={Won K. Park}, journal={arXiv: Complex Variables}, year={1999} }

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.

## 4 Citations

### Analytic continuation of a biholomorphic mapping

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We present a new proof of Pinchuk's theorem on the analytic continuation of a biholomorphic mapping from a strongly pseudoconvex analytic real hypersurface to a compact strongly pseudoconvex analytic…

### Normal forms of real hyepersurfaces with nondegenerate Levi form

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We present a proof of the existence and uniqueness theorem of a normalizing biholomorphic mapping to Chern-Moser normal form. The explicit form of the equation of a chain on a real hyperquadric is…

### Analytic Continuation of a Biholomorphic Mapping Contents

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0. Introduction and Preliminary 2 0.1. Existence and uniqueness theorem 2 0.2. Equation of a chain 7 1. Nonsingular matrices 9 1.1. A family of nonsingular matrices 9 1.2. Sufficient condition for…

### Biholomorphic mapping on the boundary I

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We study on the biholomorphic equivalence of a strongly pseudoconvex bounded domain with differentiable spherical boundary to an open ball, and we study on the biholomorphicity of a proper…

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We present a new proof of Pinchuk's theorem on the analytic continuation of a biholomorphic mapping from a strongly pseudoconvex analytic real hypersurface to a compact strongly pseudoconvex analytic…

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We present a proof of the existence and uniqueness theorem of a normalizing biholomorphic mapping to Chern-Moser normal form. The explicit form of the equation of a chain on a real hyperquadric is…