Invariant surfaces in the homogeneous space Sol with constant curvature

DOI10.1002/MANA.201010083zbMath1293.53076OpenAlexW2109937726WikidataQ125813140 ScholiaQ125813140MaRDI QIDQ5169945

Marian Ioan Munteanu, Rafael López

Publication date: 16 July 2014

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201010083

zbMATH Keywords

mean curvaturehomogeneous spaceGaussian curvatureinvariant surface

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (8)

Surfaces in \(\mathrm{Sol}_3\) space foliated by circles ⋮ Parabolicity of invariant surfaces ⋮ Invariant translators of the solvable group ⋮ Simons type formulas for surfaces in Sol₃ and applications ⋮ Minimal translation surfaces in Sol\(_{3}\) ⋮ Unnamed Item ⋮ Geodesics on an invariant surface ⋮ Loxodromes on invariant surfaces in three-manifolds

Cites Work

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• Invariant surfaces with constant mean curvature in \(\mathbb H^2 \times \mathbb R\)
• Totally umbilic surfaces in homogeneous 3-manifolds
• Invariant surfaces of the Heisenberg groups
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• Invariant surfaces of a three-dimensional manifold with constant Gauss curvature
• Flat translation invariant surfaces in the 3-dimensional Heisenberg group
• A Weierstrass type representation for minimal surfaces in Sol
• Left invariant metrics and curvatures on simply connected three-dimensional Lie groups
• Generalized pointwise symmetric Riemannian spaces: a classification
• INVARIANT CMC SURFACES IN ${\mathbb H}^2\times {\mathbb R}$
• Generalized symmetric spaces

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