On the real-analyticity of rigid spherical hypersurfaces in mathbb\n C²

2019/03/04 by Alexander Isaev, Isaev, Alexander, Joël Merker +1
Mathematics · #32V05 #35J46 #35J48 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1903.01174

openalex publication_date 2019/03/04 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We prove that every smooth rigid spherical hypersurface in mathbb C² is\nin fact real-analytic. As an application of this result, it follows that the\nclassification of real-analytic rigid spherical hypersurfaces in mathbb\nC² found by V. Ezhov and G. Schmalz applies in the smooth case.\n

Related

• Nonrigid spherical real analytic hypersurfaces in C²
• Sphericity of a real hypersurface via projective geometry
• Extremal discs and Segre varieties for real-analytic hypersurfaces in ℂ²
• Analytic Differential Equations and Spherical Real Hypersurfaces
• A short proof of the Dimension Conjecture for real hypersurfaces in \mathbb C²