arXiv subjects
Publications and source records attributed to Akın Alkan.
In this paper, we study slant helix (or $\overset{\_}ξ_{2}$-helix) and Darboux helix in Myller configuration $M$. We show that a curve in $M$ is a slant helix if and only if it is a Darboux helix. We give the alternative frame of a curve in $M$. Furthermore, we obtain the differential equations characterizing the curves in $M$ by means of both Frenet type frame and alternative frame.
A new kind of partner curve called osculating mate of a Frenet curve is introduced. Some characterizations for osculating mate are obtained and using the obtained results some special curves such as slant helix, spherical helix, $C$-slant helix and rectifying curve are constructed.
Some new kinds of special curves called $\overset{\_}ξ$-helix, $\overset{% \_}ξ_{1}$-helix, $\overset{\_}μ$-helix, $\overset{\_}ν$-helix and $W_{k}$-Darboux helices $(k\in \left\{ {n,r,o}\right\} )$ in the Myller configuration $M(C,\overset{\_}{ξ},π)$ are defined and studied. The necessary and sufficient conditions for these curves are obtained, also the axes of those helices are given and the relationships between them are introduced.