Approximations of Parallel Surfaces Along Curves

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Köse B., YAYLI Y.

International Electronic Journal of Geometry, vol.16, no.2, pp.715-726, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.36890/iejg.1362590
  • Journal Name: International Electronic Journal of Geometry
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.715-726
  • Keywords: curves on surfaces, developable surfaces, flat approximations, normal approximations, Parallel surfaces
  • Open Archive Collection: AVESIS Open Access Collection
  • Ankara University Affiliated: Yes

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.