Rotational surfaces in a pseudo-Riemannian 3-sphere
Let \(S^ 3_ 1(c)\) be a pseudo-Riemannian 3-sphere of constant positive sectional curvature c. For every constant \(h>1\) the author constructs some families of complete, space-like, rotational surfaces in \(S^ 3_ 1(1)\) with constant mean curvature h, none of which are umbilical. According to a theorem of \textit{K. Akutagawa} (On space-like hypersurfaces with constant mean curvature in the de Sitter space, preprint), if M is a complete, space-like hypersurface with constant mean curvature h in \(S^ 3_ 1(c)\) such that \(| h| \leq c^{1/2}\) then M is totally umbilical. Thus the author's construction shows that the estimate is sharp.
scientific article; zbMATH DE number 3951495