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arXiv · 2510.17030

Constant curvature hypersurfaces of cylinders over space forms

Arnando Carvalho·Ruy Tojeiro
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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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Arnando Carvalho, Ruy Tojeiro. 2025-10-19. Constant curvature hypersurfaces of cylinders over space forms. https://doi.org/10.1016/j.difgeo.2026.102415

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