Esra Betul Koc Ozturk

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 Smarandache Curves Lying in Lightcone in Minkowski 3-Space

Abstract In this paper we define the spacelike and the null lightcone Smarandache curves of a spacelike lightcone curve α according to the lightcone Frenet frame of a α in Minkowski 3-space. We obtain the lightcone curvature and the expressions for the lightcone Frenet frames vectors of a spacelike Smarandache curve of α. We prove that if the null straight line is the lightcone Smarandache curve of α, then α has non-zero constant lightcone curvature. Finally, we give some examples of lightcone Smarandache curves.

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.