Shape Operator via Darboux Frame Curvatures and Its Applications


Duldul B. U. , DÜLDÜL M.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, vol.12, no.2, pp.182-187, 2019 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2019
  • Title of Journal : INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Page Numbers: pp.182-187

Abstract

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.