On Smarandache Curves Lying in Lightcone in Minkowski 3-Space

Abstract

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