Twisted Surfaces Family in Euclidean 3-Space

Abstract

In this study, we examine a distinct set of twisted surfaces in the three-dimensional Euclidean space E3. Our focus lies in the investigation of the differential geometry of this surface family, including the determination of their curvatures. Furthermore, we establish the essential conditions for minimal surfaces within this framework. Additionally, we calculate the Laplace−Beltrami operator for this particular surface family and provide an illustrative example.