Generalized normal ruled surface of a curve in the Euclidean 3-space

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KAYA O., Önder M.

Acta Universitatis Sapientiae, Mathematica, vol.13, no.1, pp.217-238, 2021 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.2478/ausm-2021-0013
  • Journal Name: Acta Universitatis Sapientiae, Mathematica
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.217-238
  • Keywords: helix, minimal surface, normal ruled surface, slant ruled surface
  • Open Archive Collection: AVESIS Open Access Collection
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space E3. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal (equivalently, helicoid). We examine the conditions for the curves lying on this surface to be asymptotic curves, geodesics or lines of curvature. Finally, we obtain the Frenet vectors of generalized normal ruled surface and get some relations with helices and slant ruled surfaces and we give some examples for the obtained results.