Constant curvature hypersurfaces of cylinders over space forms

2025/10/19 by Arnando Carvalho, Alipio Carvalho, Arnando N.S. Carvalho +3
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Advanced Differential Geometry Research

paper · pdf · doi:10.1016/j.difgeo.2026.102415

Abstract

We classify the hypersurfaces of dimension n >= 3 with constant sectional curvature in the product spaces R^k x S^n-k+1 and R^k x H^n-k+1, for 2 <= k <= n-1. Our results provide a complete description of these hypersurfaces and extend previous classifications of constant curvature submanifolds in product spaces of space forms.

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