Invariant surfaces with constant mean curvature in \(\mathbb H^2 \times \mathbb R\)

DOI10.1007/S10231-007-0061-2zbMath1223.53048OpenAlexW1970841106MaRDI QIDQ931368

Irene Ignazia Onnis

Publication date: 25 June 2008

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-007-0061-2

zbMATH Keywords

minimal surfacesconstant mean curvature surfacesinvariant surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (12)

Rotational surfaces with prescribed mean curvature in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ Invariant translators of the solvable group ⋮ Constant mean curvature hypersurfaces in \(\mathbb{H}^n \times \mathbb{R}\) with small planar boundary ⋮ All solutions of the CMC-equation in \({\mathbb H^n\times\mathbb R}\) invariant by parabolic screw motion ⋮ A geometrical correspondence between maximal surfaces in anti-de Sitter space-time and minimal surfaces in \(\mathbb H^2\times\mathbb R\) ⋮ Cylinders as left invariant CMC surfaces in \(\operatorname{Sol}_3\) and \(E(\kappa,\tau)\)-spaces diffeomorphic to \(\mathbb{R}^3\) ⋮ Invariant surfaces in the homogeneous space Sol with constant curvature ⋮ Hypersurfaces with constant principal curvatures in \(\mathbb{S}^n\times\mathbb{R}\) and \(\mathbb{H}^n\times\mathbb{R}\) ⋮ Geodesics on an invariant surface ⋮ Loxodromes on invariant surfaces in three-manifolds ⋮ Biharmonic curves on an invariant surface ⋮ Bour's theorem and helicoidal surfaces with constant mean curvature in the Bianchi-Cartan-Vranceanu spaces

Cites Work

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• Screw motion surfaces in \(\mathbb H^2 \times \mathbb R\) and \(\mathbb S^2\times \mathbb R\)
• Invariant surfaces of the Heisenberg groups
• SO(2)-invariant minimal and constant mean curvature surfaces
• Invariant surfaces of a three-dimensional manifold with constant Gauss curvature
• INVARIANT CMC SURFACES IN ${\mathbb H}^2\times {\mathbb R}$

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