Weingarten rotation surfaces in 3-dimensional de Sitter space

Abstract.

In the 3-dimensional de Sitter Space $\textbf{S}^{3}_{1}$ , a surface is said to be a spherical (resp. hyperbolic or parabolic) rotation surface, if it is a orbit of a regular curve under the action of the orthogonal transformations of the 4-dimensional Minkowski space $\textbf{S}^{3}_{1}$ which leave a timelike (resp. spacelike or degenerate) plane pointwise fixed. In this paper, we give all spacelike and timelike Weingarten rotation surfaces in $\textbf{E}^{4}_{1}$.