Abstract
In this article, we look at a surface associated with real-valued functions. The surface is known as a harmonic surface, and its unit normal vector and mean curvature have been used to characterize it. We use the Bishop-Darboux frame ( B -Darboux frame) in Euclidean 3-space E 3 to study and explain the geometric characteristics of the harmonic evolute surfaces of tubular surfaces. The characterizations of the harmonic evolute surface’s ϱ and ς parameter curves are evaluated, and then, they are compared. Finally, an example of a tubular surface’s harmonic evolute surface is presented, along with visuals of these surfaces.
Highlights
Darboux frame is a differential geometric approach for evaluating curves and surfaces
In E3, the geometrical position of the points at the inverse distance in terms of multiplication of the mean curvature from the surface is known as the harmonic evolute surface of a tubular surface
The geometric features of the harmonic evolute surface of a tubular surface via B-Darboux frame have inspired us to study the geometric characteristics of the harmonic evolute surface of a tubular surface
Summary
Darboux frame is a differential geometric approach for evaluating curves and surfaces. In E3, the geometrical position of the points at the inverse distance in terms of multiplication of the mean curvature from the surface is known as the harmonic evolute surface of a tubular surface. Many researches on harmonic evolute surfaces have been published, some of which may be included here (see [4,5,6,7]). The geometric features of the harmonic evolute surface of a tubular surface via B-Darboux frame have inspired us to study the geometric characteristics of the harmonic evolute surface of a tubular surface. The tubular surface and the harmonic evolute surface generated from this surface will be compared and interpreted
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