The Associative Curve Of A Null Curve In The Minkowski 3-space

As the geometry model of relativity,there is a lot of difference between Minkowski space-time and the traditional Euclidean space.but it's just the direct results of different definition of metric,and such definition changed the original space structure,so some more concept will be needed.Depends on the character of the metric matrix,spacelike,timelike and null are used to describe the submanifolds. As a special case,null curve played an important role in relativ-ity,Hguhston and Shaw [1] suggested that the classical relativistic string is a surface or world-sheet in Minkowski space which satisfies the Lorentzian analogue of the minimal surface equa-tions. The string equations simplify to the wave equation and a couple of extra simple equations, and by solving the 2-dimensional wave equation it turns out that strings are equivalent to pairs of null curves, or a single null curve in the case of an open string.In order to know more about the null curve,we studied it's associative curve,and obtain the restricting condition on curvature function when the associative curve exist.This paper is arranged as follows:In the first part, we introduce the background and look back what have been done on this subject.The second part contains the basic knowledge of Minkowski space,and also something about the suspace.In third part,the frame of null curve will be introduced,the curvature function will be con-tained in chapter too.The fourth part contains the main results that the restrictive condition while the associative curve of a null curve exist.