Ruled surfaces in three dimensional lie groups

Güven I. A., Nurkan S.

Journal of Mathematical and Computational Science, vol.10, no.4, pp.936-955, 2020 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.28919/jmcs/4475
  • Journal Name: Journal of Mathematical and Computational Science
  • Journal Indexes: Scopus
  • Page Numbers: pp.936-955
  • Keywords: Geodesic torsion, Lie groups, Mean curvature, Normal curvature, Ruled surface
  • Uşak University Affiliated: Yes

Abstract

Motivated by a number of recent investigations, we define and investigate the various properties of the ruled surfaces depend on three dimensional Lie groups with a bi-variant metric. We give useful results involving the characterizations of these ruled surfaces. Some special ruled surfaces such as normal surface, binormal surface, tangent developable surface, rectifying developable surface and Darboux developable surface are worked. From those applications, we make use of such a work to interpret the Gaussian, mean curvatures of these surfaces and geodesic, normal curvature and geodesic torsion of the base curves with respect to these surfaces depend on three dimensional Lie groups.