content_image/318280.jpg content_image/318278.jpg content_image/318282.jpg content_image/318283.jpg content_image/318273.jpg content_image/318277.jpg
0 a$_{21}$m ( s ) V ′ ( t$_{0}$ ) = − λ ( s ) sinh θ, a$_{31}$n ( s ) W ′ ( t$_{0}$ ) = − λ ( s ) cosh θ, 

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 ). 

(ii) If we choose 

<img src='content_image/318280.jpg'>

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

<img src='content_image/318278.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 7 Let r ( s ) = (cos ( s ) , sin ( s ) , 0) be an arc-length spacelike curve 0 < s ≤ 2 π. It is easy to show that 

<img src='content_image/318282.jpg'>

<img src='content_image/318283.jpg'>

<img src='content_image/318273.jpg'>

<img src='content_image/318277.jpg'>

