doiSerbia

On k-type spacelike slant helices lying on lightlike surfaces

Öztürk Ufuk (Department Mathematics, Faculty of Science, University of Çankırı Karatekin, Çankırı, Turkey)
Nešović Emilija (Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Kragujevac, Serbia)
Koç Öztürk Esra Betul (Ankara Öncü College, Ankara, Turkey)

In this paper, we define k-type spacelike slant helices lying on a lightlike surface in Minkowski space E31 according to their Darboux frame for k  {0,1,2}. We obtain the necessary and the sufficient conditions for spacelike curves with non-null and null principal normal lying on lightlike surface to be the k-type spacelike slant helices in terms of their geodesic curvature, normal curvature and geodesic torsion. Additionally, we determine their axes and show that the Darboux frame of a spacelike curve lying on a lightlike surface coincides with its Bishop frame if and only if it has zero geodesic torsion. Finally, we give some examples.

Keywords: Spacelike curve, pseudo null curve, Darboux frame, slant helix, Minkowski space

Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174012