On Rotational Surfaces in 3-Dimensional de Sitter Space with Weingarten Condition

In this article, we study spacelike and timelike rotational surfaces in a 3-dimensional de Sitter space S-2(3) which are the orbit of a regular curve under the action of the orthogonal transformation of a 4-dimensional Minkowski space E-1(4) leaving a Riemannian plane, a Lorentzian plane or a degenerate plane pointwise fixed. First, we determine the profile curve of the rotational surfaces in S-1(3) whose the principal curvatures say kappa and lambda satisfy a certain relation kappa = f (lambda) for a continuous function f, which is called a Weingarten surface. Also, the profile curve of such surfaces are parametrized with respect to the principal curvature, not arc-length parameter. Then, we find the parametrization of the profile curve of spacelike and timelike Weingarten rotational surfaces in S-1(3) by choosing the certain relation as kappa = a lambda + b or kappa = a lambda(m) where a, b and m are constants. Under these circumstances, we classify the spacelike and timelike rotational surfaces in S-1(3) with constant mean curvature, namely minimal or maximal surfaces, or constant Gaussian curvature parametrized in terms of principal curvature.