Approximations of Parallel Surfaces Along Curves

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International Electronic Journal of Geometry
Volume:16 Issue:2
Approximations of Parallel Surfaces Along Curves

Approximations of Parallel Surfaces Along Curves

Authors : Büşra Köse, Yusuf Yayli

Pages : 715-726

Doi:10.36890/iejg.1362590

View : 182 | Download : 254

Publication Date : 2023-10-29

Article Type : Research Paper

Abstract :In this paper, we study developable surfaces which are flat and normal approximation of parallel surfaces along curves associated with three special vector fields. It is known that a surface whose points are at a constant distance along the normal of the surface is called a parallel surface. We investigate singularities of such developable surfaces. We show that under what conditions the approach surfaces are parallel. Also, we show that the approach surfaces are constant angle ruled surfaces if the curves selected on the surfaces are isophote, relatively normal-slant helix and helix.
Keywords : Parallel surfaces, developable surfaces, curves on surfaces, flat approximations, normal approximations

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