Projective-umbilic points of circular real hypersurfaces in $\mathbb C^2$

TL;DR

This paper proves that the boundary of certain circular domains in complex two-dimensional space must contain points with special tangency properties related to projective images of the sphere, revealing geometric constraints of such domains.

Contribution

It establishes the existence of projective-umbilic points on the boundaries of bounded strongly pseudoconvex complete circular domains in a2^2, a novel geometric insight.

Findings

Boundaries contain points with exceptional tangency to projective images of the sphere

Provides geometric characterization of circular domains in a2^2

Enhances understanding of complex hypersurface boundary properties

Abstract

We show that the boundary of any bounded strongly pseudoconvex complete circular domain in $\mathbb C^2$ must contain points that are exceptionally tangent to a projective image of the unit sphere.