Timelike surfaces in 3-dimensional lightlike cone

In this paper, we are concerned with timelike surfaces in lightlike cone Q 2 3 . At first we obtain the structure equations and the integrability conditions of the timelike surfaces in Q 2 3 . Then we give a Weierstrass type representation formula and a classification of homogeneous timelike surfaces in Q 2 3 . Finally, we discuss some properties and structures of the timelike surface and its associated surface (or called dual surface) in lightlike cone Q 2 3 .