Darboux Associated Curves of a Null Curve on Pseudo-Riemannian Space Forms

Jinhua Qian, Xueshan Fu and Seoung Dal Jung
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Jinhua Qian: Department of Mathematics, Northeastern University, Shenyang 110004, China
Xueshan Fu: Department of Mathematics, Jeju National University, Jeju 690-756, Korea
Seoung Dal Jung: Department of Mathematics, Jeju National University, Jeju 690-756, Korea

Mathematics, 2020, vol. 8, issue 3, 1-13

Abstract: In this work, the Darboux associated curves of a null curve on pseudo-Riemannian space forms, i.e., de-Sitter space, hyperbolic space and a light-like cone in Minkowski 3-space are defined. The relationships of such partner curves are revealed including the relationship of their Frenet frames and the curvatures. Furthermore, the Darboux associated curves of k-type null helices are characterized and the conclusion that a null curve and its self-associated curve share the same Darboux associated curve is obtained.

Keywords: null curve; Darboux associated curve; pseudo-Riemannian space form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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