On The slant helices according to Bishop frame of the timelike curve in Lorentzian space

Abstract

T.Ikawa obtained the following differential equation

$$D_{T}D_{T}D_{T}T-KD_{T}T,K=\kappa ^{2}-\tau ^{2}$$

for the c\i rcular helix which corresponds the case that the curvature $ \kappa $ and torsion $ \tau $ of timelike curve $ \alpha $ on the Lorentzian manifold $ M_{1} $ are  constant [5]. In this paper, we have defined a slant helix according to Bishop frame of the timelike curve. Furthermore, we have given some necessary and sufficent conditions for the slant helix and T.Ikawa's result is generalized to the case of the general slant helix.