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Open AccessArticle

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

1
Department of Mathematics, Northeastern University, Shenyang 110004, China
2
Department of Mathematics, Jeju National University, Jeju 690-756, Korea
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Authors to whom correspondence should be addressed.
Mathematics 2020, 8(3), 395; https://doi.org/10.3390/math8030395
Received: 3 February 2020 / Revised: 25 February 2020 / Accepted: 8 March 2020 / Published: 11 March 2020
(This article belongs to the Special Issue Riemannian Geometry of Submanifolds)
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. View Full-Text
Keywords: null curve; Darboux associated curve; pseudo-Riemannian space form null curve; Darboux associated curve; pseudo-Riemannian space form
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Qian, J.; Fu, X.; Jung, S.D. Darboux Associated Curves of a Null Curve on Pseudo-Riemannian Space Forms. Mathematics 2020, 8, 395.

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