Shape Operator via Darboux Frame Curvatures and Its Applications


Duldul B. U. , DÜLDÜL M.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.12, no.2, ss.182-187, 2019 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 12 Konu: 2
  • Basım Tarihi: 2019
  • Dergi Adı: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Sayfa Sayıları: ss.182-187

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.