k-type null slant helices in Minkowski space-time

Abstract

In this paper, we introduce the notion of a k-type null slant helices in Minkowski space-time, where k ∈ {0, 1, 2, 3}. We give necessary and sufficient conditions for null Cartan curves to be k-type null slant helices in terms of their curvatures κ2 and κ3. In particular, we characterize k-type null slant helices lying on the pseudosphere 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 null slant helices. Moreover, we prove that there are no 3-type null slant helices in Minkowski space-time.