Timelike surfaces in 3-dimensional lightlike cone

In this paper, we are concerned with timelike surfaces in lightlike cone Q23. At first we obtain the structure equations and the integrability conditions of the timelike surfaces in Q23. Then we give a Weierstrass type representation formula and a classification of homogeneous timelike surfaces in Q23. Finally, we discuss some properties and structures of the timelike surface and its associated surface (or called dual surface) in lightlike cone Q23.