Math. Commun. 20(2015), 83{95 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 2 f0; 1; 2; 3g. We give necessary and sufficient conditions for null Cartan curves to be k-type null slant helices in terms of their curvatures 2 and 3. In particular, we characterize k-type null slant helices lying on the pseudosphere S31(r). We nd 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. AMS subject classications: 53C40, 53C50 Key words: null Cartan curve, k-type null slant helix, Minkowski space-tim