On the Harmonic Evolute Surfaces of Hasimoto Surfaces

Abstract

In this study, firstly by considering the evolution of a moving space curve, we give some related definitions and some new results about Hasimoto surfaces in Euclidean 3-spaces.Secondly, we examine harmonic evolute surfaces of Hasimoto surfaces in Euclidean 3-spaces and also, we give some geometric properties of these type surfaces. Moreover, we express the properties of parameter curves of harmonic evolute surfaces in Euclidean space. Finally, we give an explicit example of Hasimoto surface and its harmonic evolute surface and also we plot these 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.…”

On the Hasimoto Surfaces in Euclidean 3-Space

“…Kelleci et al [5] and Elzawy [6] worked on Hasimoto surfaces in detail. Using Hasimoto surfaces, both parallel surfaces and harmonic evolute surfaces were recently obtained and characterizations of these surfaces were given in Euclidean 3-space [7,8].…”