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

Abstract

In this paper we classify the complete rotational special Weingarten surfaces in and ; i.e. rotational surfaces in and whose mean curvature H and extrinsic curvature K (e) satisfy H = f(H (2) - K (e) ), for some function such that f(0) = 0 and 4x(f'(x))(2) < 1 for any x a parts per thousand yen 0. Furthermore we show the existence of non-complete examples of such surfaces.