content_image/300903.jpg content_image/300899.jpg content_image/300900.jpg content_image/300901.jpg content_image/300898.jpg content_image/300902.jpg
function λ ( s ) ̸ = 0 such that 

<img src='content_image/300903.jpg'>

Secondly, since S ( T ) = ωT, ω ̸ = 0 , 

where s$_{0}$ is the starting value of arc length and θ = θ ( s ) . In this paper, we assume s$_{0}$ = 0 . 

Combining (4.2), (4.3) and (4.4), we have the following theorem. 

Theorem 6 A spacelike curve r ( s ) with timelike binormal is a line of curvature on the surface P ( s, t ) if and only if the followings are satisfied 

<img src='content_image/300899.jpg'>

<img src='content_image/300900.jpg'>

<img src='content_image/300901.jpg'>

Now, we analyse two different types of the marching-scale functions u ( s, t ) , v ( s, t ) and w ( s, t ) in the Eq. (4.1). 

(i) If we choose 

<img src='content_image/300898.jpg'>

is a line of curvature on the surface P ( s, t ) as 

<img src='content_image/300902.jpg'>

