The Classification Of Generalized Constant Ratio Timelike Surfaces In Minkowski 3-Space

Let x:Mâ†'R13 be a surface immersed in the 3-dimensional Minkowski space R13. If the tangential component of the position vector remains a principal direction on the surface, we call the surface generalized constant ratio surface.In this paper, we study those generalized constant ratio timelike surfaces in R13, our main results are as follows:(1) We deduce the equivalent condition for the projection vector U of the reduced position vector x/μ being a principal direction, where μ>0 is a smooth function on M. (2) We achieve a complete classification of those timelike surfaces in R13.