Generalized parallel pi-equidistant ruled surfaces

Abstract

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