Kenmotsu-Bryant type representation formula for constant mean curvature spacelike surfaces in \({\mathbf H}_1^3(-c^2)\)

DOI10.1016/S0926-2245(98)00024-2zbMath0921.53028OpenAlexW2089085624WikidataQ115337472 ScholiaQ115337472MaRDI QIDQ1295471

Reiko Aiyama, Kazuo Akutagawa

Publication date: 5 September 1999

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0926-2245(98)00024-2

zbMATH Keywords

harmonic maprepresentation formulaanti-de Sitter \(3\)-spaceconstant mean curvature spacelike surface

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Harmonic maps, etc. (58E20)

Related Items (3)

Timelike surfaces of constant mean curvature \(\pm 1\) in anti-de Sitter 3-space \(\mathbb H^3_1(-1)\) ⋮ Kenmotsu-Bryant type representation formula for constant mean curvature spacelike surfaces in \({\mathbf H}_1^3(-c^2)\) ⋮ Minimal maps between the hyperbolic discs and generalized Gauss maps of maximal surfaces in the anti-de-Sitter 3-space

Cites Work

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• Spacelike constant mean curvature surfaces in pseudo-Riemannian space forms
• A note on harmonic maps between surfaces
• Surfaces in Lorentzian hyperbolic space
• Weierstrass formula for surfaces of prescribed mean curvature
• Kenmotsu-Bryant type representation formulas for constant mean curvature surfaces in \(\mathbb{H}^3 (-c^2)\) and \(\mathbb{S}_1^3 (c^2)\)
• Kenmotsu-Bryant type representation formula for constant mean curvature spacelike surfaces in \({\mathbf H}_1^3(-c^2)\)
• Kenmotsu type representation formula for surfaces with prescribed mean curvature in the 3-sphere
• The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space
• Harmonic maps and associated maps from simply connected Riemann surfaces into the 3-dimensional space forms
• Complete minimal surfaces in \(S^ 3\)
• The Gauss Map of Surfaces in R³ and R⁴
• A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.

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