SURFACES FAMILY WITH COMMON SMARANDACHE GEODESIC CURVE

Şaffak Atalay G., Kasap E.

JOURNAL OF SCIENCE AND ARTS, no.4, pp.651-664, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2017
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.651-664
  • Keywords: Geodesic Curve, Smarandache Curves, Frenet Frame, Ruled Surface, PARAMETRIC REPRESENTATION, PENCIL, LINE
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we analyzed the problem of finding a surfaces family through a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we constructed a differential equation system such that a given Smarandache curves satisfy both the geodesic and isoparametric requirements. The extension to ruled surfaces is also outlined. Finally, we demonstrated some interesting surfaces about subject.