k-type null slant helices in Minkowski space-time

Abstract

In this paper, we introduce a notion of a $k$-type null slant helices inMinkowski space-time, where $k\in \{0,1,2,3\}$. We give the necessary andsufficient conditions for null Cartan curves to be $k$-type null slanthelices in terms of their curvatures $\kappa _{2}$ and $\kappa _{3}$. Inparticular, we characterize $k$-type null slant helices lying inpseudosphere $S^{3}_{1}(r)$. We find the relationships between $0$-type and $%1$-type null slant helices, as well as between $1$-type and $2$-type nullslant helices. Moreover, we prove that there are no $3$-type null slanthelices in Minkowski space-time.