Ufuk Öztürk

On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space

We define pseudohyperbolical Smarandache curves according to the Sabban frame in Minkowski 3-space. We obtain the geodesic curvatures and the expression for the Sabban frame vectors of special pseudohyperbolic Smarandache curves. Finally, we give some examples of such curves.

On T-slant, N-slant and B-slant helices in pseudo-Galilean space G13

In this paper, we introduce T-slant, N-slant and B-slant helices in the pseudo-Galilean space G3 and define an angle between the spacelike and the timelike isotropic vector lying in the pseudo-Euclidean plane x = 0. In particular, we obtain the explicit parameter equations of the T-slant helices and prove that there are no N-slant and B-slant helices in G3. We also prove that there are no Darboux helices in the same space.

Motions of Curves in the Pseudo-Galilean Space

We study the flows of curves in the pseudo-Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and intrinsic quantities of the inelastic flows of curves are independent of time. We show that the motions of curves in the pseudo-Galilean 3-space and its equiform geometry are described by the inviscid and viscous Burgers’ equations.

Smarandache Curves according to Curves on a Spacelike Surface in Minkowski 3-Space

We introduce Smarandache curves according to the Lorentzian Darboux frame of a curve on spacelike surface in Minkowski 3-space . Also, we obtain the Sabban frame and the geodesic curvature of the Smarandache curves and give some characterizations on the curves when the curve α is an asymptotic curve or a principal curve. And we give an example to illustrate these curves.