On Special Curves of General Hyperboloid in $ E_{1}^{3}$

Abstract

In this work, we give the Darboux vectors $\{\gamma \left( s\right) ,T\left( s\right) ,Y\left( s\right)\}$ of a given curve using the hyperbolically motion and hyperbolically inner product defined by Simsek and Özdemir in \cite{ozd}. Then, we present the variations of the geodesic curvature function $\kappa _{g}(s,w)$ and the speed function $v(s,w)$ of the curve $ \gamma $ at $w=0 $. Also, we define the new type curves whose Darboux frame vectors of a given curve makes a constant angle with the constant Killing vector field and also we obtain the parametric characterizations of these curves. At the end of this article, we exemplify these curves on the general hyperboloid with their figures using the program Mathematica.

Keywords

• General hyperboloid,Special curves,Euclidean space,Darboux frame

References

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