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.
Highlights
The geometry in Minkowski space is very important and interesting in both mathematics and physics
In 1998, Nersessian and Romos [2,3] have shown the importance of null curves in physics and mathematics by showing that there exists a geometric particle model associated with null curves in Minkowski space
Let r = r (s) : I → E31 be a null curve with Frenet frame { T, N, B} and null curvature κ (s) > 0, r (s) its Darboux associated curve on S21 with Frenet frame {α, β, γ} and curvature κ (s)
Summary
The geometry in Minkowski space is very important and interesting in both mathematics and physics. The geometry of null curves has no Riemannian analogs because one can not define the arc length parameter of null curves in a natural way due to the norm of the light-like vector vanishing everywhere. In 1998, Nersessian and Romos [2,3] have shown the importance of null curves in physics and mathematics by showing that there exists a geometric particle model associated with null curves in Minkowski space. The Darboux associated curves of a null curve on three pseudo-Riemannian space forms are defined and studied. Throughout this paper, all geometric objects under consideration are smooth and regular unless otherwise stated
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
