Laplace invariants in hypersurfaces parametrized by lines of curvature

• Autores: Carrión Riveros, Carlos, Vásquez Corro, Armando
• Formato: artículo
• Fecha de Publicación: 2017
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revista UNITRU - Selecciones Matemáticas
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/1422
• Enlace del recurso: http://revistas.unitru.edu.pe/index.php/SSMM/article/view/1422
• Nivel de acceso: acceso abierto
• Materia: Laplace invariants; Dupin hypersurfaces; lines of curvature; Invariantes de Laplace; hipersuperficies de Dupin; líneas de curvatura

In this work, using the Laplace invariants theory we give other proof for the following result: A proper Dupin hypersurfaces Mn for n ≥ 4 in Rn+1 with n distinct principal curvatures andconstant mobius curvature, cannot be parametrized by lines of curvature. Also, we study special classes of hypersurfaces Mn; n ≥ 3; in Rn+1, parametrized by lines of curvature with n distinct principal curvatures and we obtain a geometric relation when the Laplace invariants are vanish, we show that the foliations of Mn are umbilical hypersurfaces if and only if mijk = 0. Moreover, the foliations of Mn are Dupin hypersurfaces if and only if mij = 0.