Vector fields and planes in E-4 which play the role of Darboux vector


Düldül M.

TURKISH JOURNAL OF MATHEMATICS, vol.44, no.1, pp.274-283, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1908-9
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.274-283

Abstract

In this paper, we define some new vector fields along a space curve with nonvanishing curvatures in Euclidean 4-space. By using these vector fields we determine some new planes, curves, and ruled hypersurfaces. We show that the determined new planes play the role of the Darboux vector. We also show that, contrary to their definitions, osculating curves of the first kind and rectifying curves in Euclidean 4-space can be considered as space curves whose position vectors always lie in a two-dimensional subspace. Furthermore, we construct developable and nondevelopable ruled hypersurfaces associated with the new vector fields in which the base curve is always a geodesic on the developable one.