Invariant surfaces in \(\widetilde{\mathrm{PSL}}_{2}(\mathbb R, \tau)\) and applications
The author uses a 4-dimensional isometry group of a Riemannian homogeneous 3-manifold as a Riemannian fibration over a 2-manifold with curvature equal to -1 and bundle curvature of the fibration different than 0 to study the geometric behavior of surfaces having constant mean curvature and invariant under certain one-parameter group of isometries. A number of examples is given. More precisely, the author studies rotational surfaces with constant mean curvature, minimal surfaces invariant under rotations, surfaces invariant under parabolic isometries, and surfaces invariant under hyperbolic isometries. Some theorems about existence of such surfaces are presented. Moreover, applications for rotational complete surfaces having constant mean curvature equal to \(1/2\) are developed.
scientific article; zbMATH DE number 6121425
scientific article