Generalized parallel <i>p<sub>i</sub></i>-equidistant ruled surfaces

Abstract

In this paper, parallel pi-equidistant ruled surfaces in 3-dimensional Euclidean space E3, [6], were generalized to n-dimensional Euclidean space En. Then mean curvatures, Lipschitz–Killing curvatures, Gauss curvatures, scalar normal curvatures, Riemannian curvatures, Ricci curvatures, scalar curvatures of (m + 1)-dimensional parallel pi-equidistant ruled surfaces were calculated and some relations between these curvatures were found. Also, examples related to the parallel p3-equidistant ruled surfaces in the E3 are given.