Algebraic torus actions on affine algebraic surfaces

We investigate smooth affine surfaces with -actions and -fibrations. We consider a smooth affine surface with an untwisted -fibration over the affine line, and obtain a characterization of the fibration is unique in terms of the boundary divisor of the surface. As an application of the characterization, we know that a smooth affine surface admitting two independent -actions is isomorphic to or unless S has an -fibration over .