On the Cartan Curvatures of a Null Curve in Minkowski Spacetime

Abstract

We reconstruct the Cartan frame of a null curve in Minkowski spacetime for an arbitrary parameter, and we characterize pseudo-spherical null curves and Bertrand null curves. (2000). 53B30, 53A04. Mathematics Subject Classifications

Pseudo-Spherical Null Quaternionic Curves in Minkowski Space R14

“…We use the null quaternionic Cartan frame (and the null quaternionic Cartan curvatures), use them to generate pseudo sphere null quaternionic curves in Minkowski space and investigate its properties. Here, by using the similar idea of Çöken and Çiftçi [4], we show that a null quaternionic curve is a a pseudo-spherical curve if and only if (p − τ ) is a nonzero constant.…”

“…Thus, one can use these fundamental results as the basic tools in researching the geometry of null curves. The theory of Frenet frames for a null curve has been studied and developed by several researchers in this field [2][3][4]. In [4] Çöken and Çiftci have studied null curves in the 4-dimensional Minkowski space R 4 1 , and have characterized pseudo-spherical null curves.…”

“…The theory of Frenet frames for a null curve has been studied and developed by several researchers in this field [2][3][4]. In [4] Çöken and Çiftci have studied null curves in the 4-dimensional Minkowski space R 4 1 , and have characterized pseudo-spherical null curves. Recently Duggal and Jin [2] have studied the geometry of null curves and their physical use.…”

On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime

“…In the circumstances, Frenet equations associated with the Frenet frame {t(s), η(s), n 1 (s), n 2 (s)} are given by(see also [3])…”

“…Then, the pseudo-sphere having five-point contact with γ is called the osculating pseudo-sphere of γ(Ref. [3]). …”