A complete classification of parallel surfaces in three-dimensional homogeneous spaces

DOI10.1007/s10711-007-9222-0zbMath1136.53016OpenAlexW2065762385MaRDI QIDQ2481653

Jun-Ichi Inoguchi, Joeri Van der Veken

Publication date: 14 April 2008

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-007-9222-0

zbMATH Keywords

surfaceLie grouphomogeneous spaceparallel second fundamental form

Mathematics Subject Classification ID

Global submanifolds (53C40) Local submanifolds (53B25)

Related Items (12)

Sub-Lorentzian geometry of curves and surfaces in a Lorentzian Lie group ⋮ Gauss-Bonnet theorem in the universal covering group of Euclidean motion group \(E(2)\) with the general left-invariant metric ⋮ Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces ⋮ The sub-Riemannian limit of curvatures for curves and surfaces and a Gauss-Bonnet theorem in the group of rigid motions of Minkowski plane with general left-invariant metric ⋮ COMPLETE CLASSIFICATION OF PARALLEL LORENTZIAN SURFACES IN LORENTZIAN COMPLEX SPACE FORMS ⋮ Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds ⋮ Complete classification of parallel spatial surfaces in pseudo-Riemannian space forms with arbitrary index and dimension ⋮ Complete explicit classification of parallel Lorentz surfaces in arbitrary pseudo-Euclidean spaces ⋮ The classification of totally umbilical surfaces in homogeneous 3-manifolds ⋮ Some Berwald spaces of non-positive flag curvature ⋮ LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES ⋮ On rigidity phenomena of compact surfaces in homogeneous $3$-manifolds

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• Higher order parallel surfaces in the Heisenberg group
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• Stable minimal surfaces in \(M\times \mathbb R\)
• Parallel surfaces in the real special linear gorup SL (2,ℝ)
• Minimal surfaces in 3-dimensional solvable Lie groups II
• Generalized symmetric spaces

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