The Lightcone Gauss Map And The Singularity Of A Timelike Curve In R₂～4 Space

In this paper,we considered the problem of the timelike curve in R₂⁴ .We established the local theories of the curves which are in the semi-Euclidean 4-space, especially ,we considered some special ones of the timelike curve.We defined the S_t¹ × S_s¹-valued lightcone Gauss map and height function, then with the theories of the singularity we classified the singularities of the curves .Moreover, we discussed the relationships between the geometric invariantsof the timelike curve and the sin-gulatities under the action of Lorentz group as an application of unfolding theory of functions.