Extended Darboux frame field in Minkowski space-time $mathbb{E}^4_1$

Bahar Uyar Düldül1*

doi:10.26637/MJM0603/0002

Extended Darboux frame field in Minkowski space-time $mathbb{E}^4_1$

Authors :

Bahar Uyar Düldül^1*

Author Address :

¹Yildiz Technical University, Education Faculty, Department of Mathematics and Science Education, Istanbul, Turkey.

*Corresponding author.

Abstract :

In this paper, we extend the Darboux frame field along a non-null curve lying on an orientable non-null hypersurface into Minkowski space-time $mathbb{E}^4_1$ in two cases which the curvature vector and the normal vector of the hypersurface are linearly independent or dependent. Then the normal curvature, the geodesic curvature(s), and the geodesic torsion(s) of the hypersurface are given when the curve lying on the hypersurface is an asymptotic or geodesic curve.

Keywords :

Curves on hypersurface, Darboux frame field, curvatures, Minkowski space-time.

DOI :

10.26637/MJM0603/0002

Article Info :

Received : March 24, 2018; Accepted : May 09, 2018.