ϵ-isothermic surfaces in pseudo-Euclidean 3-space

• Autores: V. Corro, Armando M., C. Riveros, Carlos M., Ferro, Marcelo L.
• Formato: artículo
• Fecha de Publicación: 2023
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: inglés
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/5322
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5322
• Nivel de acceso: acceso abierto
• Materia: Dupin surfaces, Isothermic surfaces, lines of curvature.

In this paper, we provide a class of surfaces called ϵ-isothermic surface in the pseudo-Euclidean 3-space and we introduce the pseudo-Calapso equation. We prove that for each ϵ-isothermic surface, we can associate two solutions to the pseudo-Calapso equation. In particular, we associate solutions to the Calapso, Zoomeron and Davey-Stewartson III equations. In sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having distinct principal curvatures and provide explicit coordinates for such surfaces. As application of the theory, we obtain explicit solutions to the pseudo-Calapso equation and from these solutions, we provide new explicit solutions of the Zoomeron and Davey-Stewartson III equations. Moreover, we also provide explicit solutions to these equations that depend on ϵ2−holomorphic functions.