Hypersurfaces with a parallel higher fundamental form

DOI10.1007/s00022-013-0203-1zbMath1297.53019OpenAlexW1973331911MaRDI QIDQ742518

Steven Verpoort

Publication date: 18 September 2014

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-013-0203-1

zbMATH Keywords

second fundamental formshape operatorparallel hypersurfaceBianchi-Cartan-Vranceanu spacethree-dimensional homogeneous space

Mathematics Subject Classification ID

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

Related Items (2)

Constant mean curvature isometric immersions into \(\mathbb{S}^2\times\mathbb{R}\) and \(\mathbb{H}^2\times\mathbb{R}\) and related results ⋮ Isoparametric surfaces in $E(\kappa,\tau)$-spaces

Cites Work

• Constant angle surfaces in the Heisenberg group
• Complete constant mean curvature surfaces in homogeneous spaces
• Grassmann geometry on the 3-dimensional unimodular Lie groups. I
• Isometric immersions into 3-dimensional homogeneous manifolds
• Higher order parallel surfaces in Bianchi-Cartan-Vranceanu spaces
• The classification of hypersurfaces of a Euclidean space with parallel higher order fundamental form
• Symmetric submanifolds of Euclidean space
• On symmetric submanifolds of spaces of constant curvature
• The third fundamental form metric for hypersurfaces in nonflat space forms
• Invariant surfaces of the Heisenberg groups
• Immersions with parallel second fundamental form
• Total bending of vector fields on Riemannian manifolds
• Higher order parallel submanifolds of a complex space form
• On the Three-Dimensional Homogenous SO(2)-Isotropic Riemannian Manifolds
• A characterization of locally homogeneous Riemann manifolds of dimension 3
• A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ₁= ρ₂≠ ρ₃
• Three-dimensional Riemannian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3
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