Relatively normal-slant helices in Minkowski $3$-space

Abstract

In this paper, we study relatively normal-slant helices lying on timelike as well as spacelike surfaces in Minkowski $3$-space ${\mathbb{E}}_1^3$. The axes of spacelike and timelike relatively normal-slant helices are obtained via their Darboux frames. We also establish characterization theorems for spacelike and timelike relatively normal-slant helices in Minkowski $3$-space ${\mathbb{E}}_1^3$. Finally, the relationship between relatively normal-slant helices and slant helices is found on timelike as well as spacelike surfaces.