Closed generalized elastic curves in \({\mathbf S}^{2}\)(1).

DOI10.1016/S0393-0440(03)00047-0zbMath1045.53002MaRDI QIDQ1414655

Óscar J. Garay, Josu Arroyo, José J. Mencía

Publication date: 4 December 2003

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

zbMATH Keywords

curvatureelastic curvesvariation formulacurvature energy functional

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Curves in Euclidean and related spaces (53A04) Local Riemannian geometry (53B20) Existence theories for free problems in one independent variable (49J05)

Related Items (19)

Generalized elastic line deformed on a nonnull surface by an external field in the 3-dimensional semi-Euclidean space \(\mathbb{E}_{1}^{3}\) ⋮ Unnamed Item ⋮ Kinematics of hypersurfaces in Riemannian manifolds ⋮ Biharmonic and biconservative hypersurfaces in space forms ⋮ Interacting charged elastic loops on a sphere ⋮ Kirchhoff elastic rods in five-dimensional space forms whose centerlines are not helices ⋮ Instability of closed p-elastic curves in 𝕊2 ⋮ Closed 1/2-elasticae in the hyperbolic plane ⋮ Spherical curves whose curvature depends on distance to a great circle ⋮ A characterization of the catenary under the effect of surface tension ⋮ Critical tori for mean curvature energies in Killing submersions ⋮ Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers ⋮ Elastic Sturmian spirals in the Lorentz-Minkowski plane ⋮ QUADRATIC CURVATURE ENERGIES IN THE 2-SPHERE ⋮ Extremals of curvature energy actions on spherical closed curves ⋮ Elastic curves with constant curvature at rest in the hyperbolic plane ⋮ GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS ⋮ Closed biconservative hypersurfaces in spheres ⋮ Closed 1/2-elasticae in the 2-sphere

Cites Work

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• [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
• Curve-straightening and the Palais-Smale condition
• Non-Euclidean Elastica
• Complete integrability for Lagrangians dependent on acceleration in a spacetime of constant curvature

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