Elasticae in Killing submersions

DOI10.1007/s00009-016-0685-9zbMath1358.58010OpenAlexW2263792744MaRDI QIDQ350209

Mohammad Hasan, M. Dambrine

Publication date: 7 December 2016

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-016-0685-9

zbMATH Keywords

Bianchi-Cartan-Vranceanu spaceselasticaeHopf cylindersKilling submersions

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Classical differential geometry (53A99) Optimality conditions (49K99)

Related Items (3)

Triharmonic curves in 3-dimensional homogeneous spaces ⋮ Elastic magnetic curves of ferromagnetic and superparamagnetic models on the surface ⋮ Totally biharmonic hypersurfaces in space forms and 3-dimensional BCV spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Locally convex surfaces immersed in a Killing submersion
• On the classification of Killing submersions and their isometries
• Extremals of curvature energy actions on spherical closed curves
• The total squared curvature of closed curves
• Isometric immersions into 3-dimensional homogeneous manifolds
• The Euler-Lagrange method for biharmonic curves
• Kirchhoff elastic rods in three-dimensional space forms
• Elasticae with constant slant in the complex projective plane and new examples of Willmore tori in five spheres
• Willmore-like tori in Killing submersions
• Exterior differential systems and the calculus of variations
• Extremal curves of the total curvature in homogeneous 3-spaces
• [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
• Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti
• General helices and a theorem of Lancret
• Non-Euclidean Elastica
• Elastica in SO(3)

This page was built for publication: Elasticae in Killing submersions