A class of surfaces with planar lines of curvature (Selecciones Matemáticas, 2021)
In this paper we study surfaces parameterized by lines of curvature. We obtain a characterization of a class of surfaces with planar lines of curvature, this characterization depend on certain holomorphic function.We present a class of surfaces with two family of planar lines of curvature, this class of surfaces includes the Dupin surfaces. Also, we give explicit examples.
Keywords: Líneas de curvatura planas; superficies de Dupin; funciones holomorfas