On Generalized Darboux Frame of a Pseudo Null Curve Lying on a Lightlike Surface in Minkowski 3-space

Year 2023, Volume: 16 Issue: 1, 81 - 94, 30.04.2023

Jelena Djordjević Emilija Nešović

https://doi.org/10.36890/iejg.1269538

Cited By: 2

Abstract

In this paper we define generalized Darboux frame of a a pseudo null curve $\alpha$ lying on a
lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that $\alpha$ has two such frames and obtain generalized Darboux frame's equations. We obtain
the relations between the curvature functions of $\alpha$ with respect to
the Darboux frame and generalized Darboux frames. We also find parameter equations of the Darboux vectors of the Frenet, Darboux and generalized Darboux frames and give the necessary and the sufficient conditions for such vectors to have the same directions. Finally, we present related examples.

Keywords

generalized Darboux frame, pseudo null curve, lightlike surface, Minkowski space

Supporting Institution

This work is partially supported by the Serbian Ministry of Education, Science and Technological Development (Agreement No. 451-03-47/2023-01/ 200122).

Project Number

Agreement No. 451-03-47/2023-01/ 200122

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