On the pedal surfaces of 2-d surfaces with the constant support function in E^4

Abstract

In this paper, we consider the pedal surface M of a 2-d surface M with the constant support function that parameter lines of M are the lines curvatures, in 4-dimensional Euclidean Space 4 E. We investigated the relations between coefficients of the first, the second and the third fundamental forms of M and M. Also, the relations between the Gauss curvatures, the Gauss torsions, the mean curvatures, the mean curvature vectors and the principal normal curvatures of M and M were obtained. Furthermore, we proved that pedal of every Aminov surface is a curve if the parameter lines of it are the lines curvatures. Finally, we drew some special surfaces and pedals of them by using parallel projection on the Maple 17 software package programing.