On Time-Like Class A Surfaces in a Static Space Time

In this paper, we consider time-like surfaces in the static space-time given by the warped product L³₁(c)\, f× (I,dz²), where L³₁(c) denotes the Lorentzian space form with the constant sectional curvature c∈\-1,0,1\. In particular, we study the surfaces with light-like (∂/∂ z)T. First, we construct a globally defined pseudo-orthonormal frame field on a surface satisfying this condition and deal with the invariants associated with this frame field. Then, we obtain a complete classification theorem for class~A surfaces. Finally, we consider some applications of this theorem.