2026/109/1-2 (3)
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DOI: 10.5486/PMD.2026.10374
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pp. 45-60
Ribaucour-type hypersurfaces
Authors:
Milton Javier Cardenas Mendez 
and Armando Mauro Vasquez Corro
Abstract:
In this work, we generalize the notion of Ribaucour-type surfaces (RT-surfaces) studied in [6] and [7] to higher dimensions and introduce Ribaucour-type hypersurfaces (RT-hypersurfaces). We obtain a representation for hypersurfaces with prescribed normal mapping. We prove that RT-hypersurfaces are determined by a real function that satisfies a second-order differential equation. As an application, we classify rotational RT-hypersurfaces.
Keywords: Ribaucour surfaces, generalized Weingarten surfaces, prescribed Gauss normal map, Weierstrass-type representation
Mathematics Subject Classification: 53A04, 53A05, 58A40