content_image/326017.jpg content_image/326023.jpg content_image/326013.jpg content_image/326021.jpg content_image/326022.jpg content_image/326014.jpg content_image/326024.jpg
λ ( s ) ̸ = 0 , where l ( s ) , m ( s ) , n ( s ) , U ( t ) , V ( t ) and W ( t ) are C 1 functions, a$_{ij}$ ∈ R ( k = 1 , 2 , 3; j = 1 , 2 , 3 , ..., p ) . 

<img src='content_image/326017.jpg'>

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

<img src='content_image/326023.jpg'>

λ ( s ) ̸ = 0 , where l ( s ) , m ( s ) , n ( s ) , U ( t ) , V ( t ) and W ( t ) are C 1 functions, a$_{ij}$ ∈ R ( k = 1 , 2 , 3; j = 1 , 2 , 3 , ..., p ). 

Example 9 Let r ( s ) = (cosh ( s ) , 0 , sinh ( s )) be an arc-length timelike curve , 0 ≤ s ≤ 2 π. It is easy to show that 

<img src='content_image/326013.jpg'>

(ii) If we choose marching-scale functions as 

<img src='content_image/326021.jpg'>

<img src='content_image/326022.jpg'>

<img src='content_image/326014.jpg'>

<img src='content_image/326024.jpg'>

