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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jinhua Qian & Xueshan Fu & Seoung Dal Jung, 2020. "Darboux Associated Curves of a Null Curve on Pseudo-Riemannian Space Forms," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:395-:d:330973
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