Classification of rotational special Weingarten surfaces of minimal type in S^2 x R and H^2 x R

Abstract: In this paper we finish the classification of rotational special Weingarten surfaces in S^2 x R and H^2 x R; i.e. rotational surfaces in S^2 x R and H^2 x R whose mean curvature h and extrinsic curvature K_e satisfy h=f(h^2-K_e), for some function f in C^1([0,+infty)) such that 4x(f'(x))^2<1 for any x>=0.