Bour's minimal surface revisited: the irreducible implicit equation of the incomplete surface

Abstract

We focus on the differential geometry of the Bour’s minimal surface inEuclidean 3-space. We also calculate the mean curvature, the Gaussiancurvature, class, degree, index, total curvature, irreducible implicit equa-tion of the incomplete algebraic minimal surface. Furthermore, we revealamazing figures.