Conformal geometry of hypersurfaces in Lorentz space forms

DOI10.1155/2013/549602zbMath1314.53099arXiv1511.07621OpenAlexW2092050878WikidataQ58919881 ScholiaQ58919881MaRDI QIDQ2260763

Tongzhu Li, ChanG Xiong Nie

Publication date: 12 March 2015

Published in: Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07621

zbMATH Keywords

conformal metricspace-like hypersurfaceWillmore hypersurfaceconformal second fundamental form

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global submanifolds (53C40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (4)

Regular space-like hypersurfaces in \(\mathbb S^{m+1}_1\) with parallel para-Blaschke tensors ⋮ Spacelike Möbius hypersurfaces in four dimensional Lorentzian space form ⋮ Time-like conformal homogeneous hypersurfaces with three distinct principal curvatures ⋮ Spacelike hypersurfaces with constant conformal sectional curvature in \(\mathbb{R}_1^{n+1}\)

Cites Work

• Willmore hypersurfaces in a sphere
• Moebius geometry of submanifolds in \(\mathbb{S}^n\)
• Willmore tori and Willmore-Chen submanifolds in pseudo-Riemannian spaces
• Möbius geometry of hypersurfaces with constant mean curvature and scalar curvature
• Willmore surfaces in \(S^n\)
• Möbius isoparametric hypersurfaces in \(S^{n+1}\) with two distinct principal curvatures
• Lorentzian isoparametric hypersurfaces
• Conformally flat Lorentzian hypersurfaces in the conformal compactification of Lorentz space
• Zero mean curvature surfaces with non–negative curvature in flat Lorentzian 4–spaces
• A conformal differential invariant and the conformal rigidity of hypersurfaces

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