Generalized parallel <i>p_i</i>-equidistant ruled surfaces

Abstract

In this paper, parallel pi-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 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 E 3 are given.