Relatively normal-slant helices lying on a surface and their characterizations

Authors : Nesibe MACİT, Mustafa DÜLDÜL

Pages : 397-408

View : 18 | Download : 5

Publication Date : 2017-06-01

Article Type : Research Paper

Abstract :In this paper, we consider a regular curve on an oriented surface in Euclidean 3-space with the Darboux frame $\{T,U,V\}$ along the curve, where $T$ is the unit tangent vector field of the curve, $U$ is the surface normal restricted to the curve and $V=T\times U$. We define a new curve on a surface by using the Darboux frame. This new curve whose vector field V makes a constant angle with a fixed direction is called as relatively normal-slant helix. We give some characterizations for such curves and obtain their axis. Besides we give some relations between some special curves insert ignore into journalissuearticles values(general helices, integral curves, etc.); and relatively normal-slant helices. Moreover, when a regular surface is given by its implicit or parametric equation, we introduce the method for generating the relatively normal-slant helix with the chosen direction and constant angle on the given surface.
Keywords : Slant helix, generalized helix, Darboux frame, implicit surface, parametric surface, spherical indicatrix