Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.

DOI10.1016/S0926-2245(02)00060-8zbMath1035.53089WikidataQ115338221 ScholiaQ115338221MaRDI QIDQ1608974

Lieven Vanhecke, José Carmelo González-Dávila

Publication date: 14 August 2002

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

zbMATH Keywords

energy minimizersKilling vector fieldsharmonic sections of the unit tangent bundle

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43)

Related Items (11)

Harmonic sections of Riemannian vector bundles, and metrics of Cheeger-Gromoll type ⋮ Harmonic almost contact structures ⋮ Magnetic unit vector fields ⋮ Harmonic sections of homogeneous fibre bundles. ⋮ Area-minimizing vector fields on round 2-spheres ⋮ Bending and stretching unit vector fields in Euclidean and hyperbolic 3-space ⋮ Harmonicity and minimality of oriented distributions ⋮ Harmonic sections normal to submanifolds and their stability ⋮ Stability of unit Hopf vector fields on quotients of spheres ⋮ Invariant harmonic unit vector fields on the oscillator groups ⋮ Stability of Left-Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the volume of a unit vector field on the three-sphere
• On harmonic vector fields
• Contact manifolds in Riemannian geometry
• Curvatures of left invariant metrics on Lie groups
• About a decomposition of the space of symmetric tensors of compact support on a Riemann manifold
• Unit vector fields on spheres, which are harmonic maps
• Relationship between volume and energy of vector fields.
• Total bending of flows with mean curvature correction
• Minimal and harmonic unit vector fields in \(G_2(\mathbb{C}^{m+2})\) and its dual space
• Harmonic and minimal vector fields on tangent and unit tangent bundles
• Examples of minimal unit vector fields
• Minimal unit vector fields
• Total bending of vector fields on Riemannian manifolds
• Total bending of vector fields on the sphere \(S^ 3\)
• The energy of Hopf vector fields
• Another Report on Harmonic Maps
• A Report on Harmonic Maps
• Volumes of Flows
• Harmonic Mappings of Riemannian Manifolds
• Curvature and Betti Numbers. (AM-32)
• On the energy of a unit vector field
• The energy of unit vector fields on the 3-sphere
• Invariant minimal unit vector fields on Lie groups
• Second variation of volume and energy of vector fields. Stability of Hopf vector fields
• Harmonic and minimal radial vector fields
• Minimality and harmonicity for Hopf vector fields

This page was built for publication: Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.