On the real-analyticity of rigid spherical hypersurfaces in ${\mathbb{C}}^2$

Abstract

We prove that every smooth rigid spherical hypersurface in ${\mathbb{C}}^2$ is in fact real-analytic. As an application of this result, it follows that the classification of real-analytic rigid spherical hypersurfaces in ${\mathbb{C}}^2$ found by V. Ezhov and G. Schmalz applies in the smooth case.