Distance-normal congruence of rotational surfaces in euclidean 3-space

Abstract

In this study, we considered simple linear congruences of some curves/surfaces to generate parametric families of curves/surfaces. The method depends essentially on the position vector of a curve/surface and its signed unit normal. The shape of the normal congruence of the curve/surface can be predictably changed based on the sign of its unit normal. On the other hand, symmetry of surfaces refers to invariance under transformations such as reflections, rotations, or translations, which can also involve normal congruence. Considering the normal congruences of the surface of revolution to be minimal, some results on the meridian curves are obtained. Furthermore, some surface models are constructed over the meridian curves.