Willmore tori and Willmore-Chen submanifolds in pseudo-Riemannian spaces

DOI10.1016/S0393-0440(98)00010-2zbMath0954.53037OpenAlexW2125293798WikidataQ115338788 ScholiaQ115338788MaRDI QIDQ1299348

Pascual Lucas, Manuel Barros, Angel Ferrández, Miguel Angel Meroño

Publication date: 8 February 2001

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

Full work available at URL: https://doi.org/10.1016/s0393-0440(98)00010-2

zbMATH Keywords

Willmore torusanti De Sitter 3-spacewarped product spaceWillmore-Chen submanifold

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (15)

Hypersurface constrained elasticae in Lorentzian space forms ⋮ CURVATURE PROPERTIES OF PSEUDO-SPHERE BUNDLES OVER PARAQUATERNIONIC MANIFOLDS ⋮ Unnamed Item ⋮ Hyperelastic Curves in 3-dimensional Lightlike Cone ⋮ Instability of closed p-elastic curves in 𝕊2 ⋮ Closed 1/2-elasticae in the hyperbolic plane ⋮ Willmore energy estimates in conformal Berger spheres ⋮ Reduction of variables for Willmore-Chen submanifolds in seven spheres ⋮ Some Variational Problems on Curves and Applications ⋮ Conformal geometry of hypersurfaces in Lorentz space forms ⋮ Extremals of curvature energy actions on spherical closed curves ⋮ A criterion for reduction of variables in the Willmore-Chen variational problem and its applications ⋮ Elasticity and conformal tension via the Kaluza-Klein mechanism ⋮ Closed 1/2-elasticae in the 2-sphere ⋮ Bosonic string theory in Lorentzian principal circle bundles over anti-de-Sitter space \(\text{AdS}_3\)

Cites Work

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• The principle of symmetric criticality
• The total squared curvature of closed curves
• Hopf tori in \(S^ 3\)
• Hopf submanifolds in \(S^7\) which are Willmore-Chen submanifolds
• Fat bundles and symplectic manifolds
• Elasticae with constant slant in the complex projective plane and new examples of Willmore tori in five spheres
• Stationary 2-type surfaces in a hypersphere
• Minimal varieties in Riemannian manifolds
• Knotted Elastic Curves in R ³
• [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
• New properties and examples of incomplete Lorentzian tori
• General helices and a theorem of Lancret
• Willmore tori in non-standard 3-spheres
• Free elasticae and Willmore tori in warped product spaces
• Free Elastic Parallels in a Surface of Revolution

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