Relatives Geometries

• Autores: Corro, Armando, Lopes Ferro, Marcelo
• Formato: artículo
• Fecha de Publicación: 2022
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: inglés
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/4501
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4501
• Nivel de acceso: acceso abierto
• Materia: Hipersuperficie relativa; Hipersuperficie de Dupin relativa; geometría isótropa; Transformación de Ribaucour; Relative hypersurface; Relative Dupin hypersurface; Isotropic geometry; Ribaucour transformations

In this paper we consider M a fixed hypersurface in Euclidean space and we introduce two types of spaces relative to M, of type I and type II. We observe that when M is a hyperplane, the two geometries coincides with the isotropic geometry. By applying the theory to a Dupin hypersurface M, we define a relative Dupin hypersurface M of type I and type II , we provide necessary and sufficient conditions for a relative hypersurface M to be relative Dupin parameterized by relative lines of curvature, in both spaces. Moreover, we provides a relationship between the Dupin hypersurfaces locally associated to M by a Ribaucour transformation and the type II Dupin hypersurfaces relative M. We provide explicit examples of the Dupin hypersurface relative to a hyperplane, torus, S1  x  Rn-1 and  S2 x  Rn-2, in both spaces.