A note on the spherical images of W-partially null curves in Minkowski space-time $\mathbb{E}_{1}^{4}$

Y. Ünlütürk, Z. Karakaş

In this study, we investigate the tangent, principal normal and trinormal spherical images of a W-partially null curve in pseudohyperbolic space $\mathbb{H}_{0}^{3}$ of Minkowski space time $\mathbb{E}_{1}^{4}$. The tangent, principal normal spherical images of a W-partially null curve occur as spacelike curves lying in pseudosphere $\mathbb{S}_{0}^{3}$, then the Frenet-Serret invariants of the mentioned image curves are obtained in terms of the invariants of W-partially null curve. The trinormal spherical images of a W-partially null curve occur as spacelike curves lying in pseudohyperbolic space $\mathbb{H}_{0}^{3}$, then the Frenet-Serret invariants of the mentioned image curves are obtained in terms of the invariants of W-partially null curve. Finally, we give some characterizations of the spherical images being helices. 

Tbilisi Mathematical Journal, Vol. 12(4) (2019), pp. 213-225