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

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KAYA O., Önder M.

Acta Universitatis Sapientiae, Mathematica, cilt.13, sa.1, ss.217-238, 2021 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.2478/ausm-2021-0013
  • Dergi Adı: Acta Universitatis Sapientiae, Mathematica
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.217-238
  • Anahtar Kelimeler: helix, minimal surface, normal ruled surface, slant ruled surface
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

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.