Shape Operator via Darboux Frame Curvatures and Its Applications

Duldul B. U., Düldül M.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.12, sa.2, ss.182-187, 2019 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 2
  • Basım Tarihi: 2019
  • Dergi Adı: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.182-187
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

We present the shape operator's matrix of a surface along a surface curve. By using the obtained matrix, we give a short proof of the Beltrami-Enneper theorem. Also, we give a new method for determining the well-known geodesic curves of a plane, a sphere and a circular cylinder by using the relation between the ordinary curvatures of the geodesic and the curvatures of the surface.