Classification of hypersurfaces with constant Möbius curvature in \({\mathbb{S}^{m+1}}\)

DOI10.1007/S00209-011-0860-4zbMath1259.53010OpenAlexW2087204766MaRDI QIDQ431293

Xiang Ma, Limiao Lin, Tongzhu Li, Zhen Guo, Chang Ping Wang

Publication date: 26 June 2012

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

Full work available at URL: https://doi.org/10.1007/s00209-011-0860-4

zbMATH Keywords

constant sectional curvatureMöbius metriccurvature-spiralMöbius deformable hypersurfacesMöbius flat hypersurfaces

Mathematics Subject Classification ID

Local submanifolds (53B25)

Related Items (10)

A Möbius scalar curvature rigidity on compact conformally flat hypersurfaces in \(\mathbb{S}^{n + 1}\) ⋮ Willmore hypersurfaces with constant Möbius curvature in \(\mathbb R^{n+1}\) ⋮ Submanifolds with semi-parallel Möbius second fundamental form in the unit sphere ⋮ Classification of hypersurfaces with constant Möbius Ricci curvature in \(\mathbb{R}^{n+1}\) ⋮ A complete classification of Blaschke parallel submanifolds with vanishing Möbius form ⋮ Conformal invariants of submanifolds in a Riemannian space and conformal rigidity theorems on Willmore hypersurfaces ⋮ Deformation of hypersurfaces preserving the Möbius metric and a reduction theorem ⋮ Unnamed Item ⋮ A Möbius rigidity of compact Willmore hypersurfaces in \(\mathbb{S}^{n+1}\) ⋮ Spacelike hypersurfaces with constant conformal sectional curvature in \(\mathbb{R}_1^{n+1}\)

Cites Work

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• Submanifolds with constant Möbius scalar curvature in \(S^n\)
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• Flat Möbius hypersurfaces in \(S^{n+1}\)
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• Classification of hypersurfaces with parallel Möbius second fundamental form in \(S^{n+1}\)
• A conformal differential invariant and the conformal rigidity of hypersurfaces
• Möbius geometry of surfaces of constant mean curvature 1 in hyperbolic space
• A Moebius characterization of Veronese surfaces in \(S^n\)
• The second variational formula for Willmore submanifolds in \(S^n\).

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