On eqiform Darboux helices in Galilean 3-space

In this paper, we define equiform Darboux helices in a Galilean space (G_{3}) and obtain their explicit parameter equations. We show that equiform Darboux helices have only a non-isotropic axis and characterize equiform Darboux vectors of equiform Darboux helices in terms of equiform rectifying curves. We prove that an equiform Darboux vector of an equiform Darboux helix α is an equiform Darboux helix if an admissible curve (alpha) is a rectifying curve. We also prove that there are no equiform curves of constant precession and give some examples of equiform Darboux helices

k-type null slant helices in Minkowski space-time

In this paper, we introduce a notion of a $k$-type null slant helices inMinkowski space-time, where $kin {0,1,2,3}$. We give the necessary andsufficient conditions for null Cartan curves to be $k$-type null slanthelices in terms of their curvatures $kappa _{2}$ and $kappa _{3}$. Inparticular, we characterize $k$-type null slant helices lying inpseudosphere $S^{3}_{1}(r)$. We find the relationships between $0$-type and $$-type null slant helices, as well as between $1$-type and $2$-type nullslant helices. Moreover, we prove that there are no $3$-type null slanthelices in Minkowski space-time

On eqiform Darboux helices in Galilean 3-space

In this paper, we define equiform Darboux helices in a Galilean space (G_{3}) and obtain their explicit parameter equations. We show that equiform Darboux helices have only a non-isotropic axis and characterize equiform Darboux vectors of equiform Darboux helices in terms of equiform rectifying curves. We prove that an equiform Darboux vector of an equiform Darboux helix α is an equiform Darboux helix if an admissible curve (alpha) is a rectifying curve. We also prove that there are no equiform curves of constant precession and give some examples of equiform Darboux helices