On the real-analyticity of rigid spherical hypersurfaces in ℂ²

Abstract

We prove that every smooth rigid spherical hypersurface in C 2 \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 C 2 \mathbb {C}^2 found by V. Ezhov and G. Schmalz applies in the smooth case.