In this study, we defined null quaternionic Bertrand curves in R₁⁴. The only Bertrand null quaternionic curves in R₁⁴ are null quaternionic helices with (p-τ)=0.
In this study, we define the osculating pseudo-sphere of a null quaternionic Cartan curve in Minkowski space R₁⁴. We give a characterization for pseudo-spherical null quaternionic Cartan curves.
In this paper, we define the harmonic curvature functions for dual quaternionic curves. Moreover, we also study some characterizations for dual quaternionic slant helices according to dual quaternionic frame.
In this study, we define null quaternionic Bertrand curves in ℝ³_{v} for a null quaternionic curve, which has a single non-zero, constant Cartan curvature τ. We also prove that if a null quaternionic curve with non-zero curvatures in ℝ³_{v} is a null quaternionic Bertrand curve, then it is a null quaternionic helix.
We define harmonic curves and inclined curves for dual split quaternionic curves. And then, we give some characterizations for dual split quaternionic inclined curves by means of the harmonic curvatures.