On the parallel surfaces of the non-developable surfaces

Al C., YAYLI Y.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, cilt.98, sa.2, ss.59-68, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 98 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.31489/2020m2/59-68
  • Dergi Adı: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.59-68
  • Anahtar Kelimeler: parallel surfaces, non-developable ruled surface, striction line, Gaussian curvature, mean curvature, curvatures of curve-surface pair, RULED SURFACES
  • Ankara Üniversitesi Adresli: Evet

Özet

In the differential geometry of curves and surfaces, the curvatures of curves and surfaces are often calculated and results are given. In particular, the results given by using the apparatus of the curve-surface pair are important in terms of what kind of surface the surface indicates. In this study, some relationships between curvatures of the parallel surface pair (X, X-r) via structure functions of non-developable ruled surface X(u, v) = a(u) + vb(u) are established such that a(u) is striction curve of non-developable surface and b(u) is a unit spherical curve in E-3. Especially, it is examined whether the non-developable surface X-r is minimal surface, linear Weingarten surface and Weingarten surface. X and its parallel X-r are expressed on the Helicoid surface sample. It is indicated on the figure with the help of SWP. Moreover, curvatures of curve-surface pairs (X, a) and (X-r , beta) are investigated and some conclusions are obtained.