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.

Keywords

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

References

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