On the Harmonic Evolute Surfaces of Tubular Surfaces in Euclidean 3-Space

Abstract

The aim of this study is to investigate and interpret the geometric properties of the harmonic evolute surfaces of the tubular surfaces in Euclidean 3-space. For this purpose, the harmonic evolute surface is defined by considering the definitions and theorems for the tubular surface constructed in the Euclidean 3-space. The characterizations of the s and ψ parameter curves of the harmonic evolute surface obtained are examined, and then parameter curves of the tubular surface and harmonic evolute surface are compared. Finally, the harmonic evolute surface of a tubular surface is given an example and the graphics of these surfaces are drawn.

The Physical Concepts on Special Tube Surfaces Generated by Normal Curves in Galilean 3-Space

“…Then, we substitute (33) and ( 34), (32) into the equation (10). Hence, the first fundamental form of the tube surface by generated normal curve in Galilean space can be written as…”

“…The tubular surface and the characterizations of the parameter curves of this surface have been investigated in Euclidean space, see [1,[10][11]. In [8], the author defined the tubular surfaces in Galilean space and the differential features of tubular surfaces.…”

On Ruled Surfaces Constructed by the Evolution of a Polynomial Space Curve

“…To solve this problem, Dede defined the Flc frame for moving polynomial curves [7,8]. The Flc frame [9][10][11][12][13] and ruled surfaces on different frames [14][15][16][17][18][19][20][21][22][23] have been investigated by many researchers. Inspired by these studies, we conducted this research to create a new resource on the subject of surfaces and to form a basis for future studies.…”