On the Harmonic Evolute Surfaces of Hasimoto Surfaces

Year 2021, Volume: 11 Issue: 1, 87 - 100, 30.06.2021

Kemal Eren , Alev Kelleci Akbay

https://doi.org/10.37094/adyujsci.820698

Cited By: 2

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.

Keywords

Hasimoto surfaces;, harmonic evolute surface;, binormal motion;, evolution of curves and surfaces;, Gaussian curvature;, mean curvature.

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