On calculation of the pitch and angle of pitch of a closed ruled surface of dimension (k + 1) using a rotation minimizing frame in Euclidean space ℝn

Abstract

In this paper, first, the pitch and the angle of pitch of a closed ruled surface of dimension (k + 1) are calculated according to a rotation minimizing frame in Euclidean space . To calculate this pitch and this angle of pitch of the closed ruled surface of dimension (k + 1), three different ruled surfaces are taken according to the rotation minimizing frame. Therefore, for these three different ruled surfaces, three different situations are found. Second, by taking any curve in four‐dimensional Euclidean space, the closed ruled surface of this curve, its orthogonal trajectory, the pitch, and the angle of pitch of this closed ruled surface are obtained according to the rotation minimizing frame. Finally, the pitch and the angle of pitch of the closed ruled surface of dimension (k + 1) are generalized to n‐dimensional Euclidean space with the help of the rotation minimizing frame.