General helices with lightlike slope axis

Abstract

In this paper, we investigate general helices with lightlike slope axis. We give necessary and sufficient conditions for a general helix to have a lightlike slope axis. We obtain parametric equation of all general helices with lightlike slope axis. Also we give a nice relation between helix with lightlike slope axis and biharmonic curves in Minkowski 3-space E 3 1 .

Slant helices in Minkowski 3-space E31 with Sasai’s modified frame fields

“…These are geodesics of cylinders shaped over a plane curve. Recently, general helices with different slope axis were investigated in [5,18,19]. Slant helices are the successor curves of the general helices [15].…”