Minimal unit vector fields

DOI10.2748/tmj/1113247180zbMath1006.53053OpenAlexW2103472729MaRDI QIDQ1607527

Elisa Llinares-Fuster, Olga Gil-Medrano

Publication date: 13 March 2003

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1113247180

zbMATH Keywords

critical pointsKilling vector fieldsminimal immersionHopf vector fieldsminimal vector fieldsvolume of vector fields

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20)

Related Items (24)

MINIMALITY, HARMONICITY AND CR GEOMETRY FOR REEB VECTOR FIELDS ⋮ Stability of the Reeb vector field of \(H\)-contact manifolds ⋮ Minimal unit vector fields with respect to Riemannian natural metrics ⋮ Instability of Hopf vector fields on Lorentzian Berger spheres ⋮ On properties of the Reeb vector field of $(\alpha,\beta)$ trans-Sasakian structure ⋮ Gauss maps of harmonic and minimal great circle fibrations ⋮ Volume and energy of Reeb vector fields ⋮ Geometry of a surface in Riemannian 3-manifold corresponding to a smooth autonomous dynamical system ⋮ Minimally immersed Klein bottles in the unit tangent bundle of the unit 2-sphere arising from area-minimizing unit vector fields on \(\mathbb{S}^2\backslash \{ N,S\}\) ⋮ Lipschitz minimality of Hopf fibrations and Hopf vector fields ⋮ Calibrations for the volume of unit vector fields in dimension 2 ⋮ Stability numbers in K-contact manifolds ⋮ Unit vector fields of minimum energy on quotients of spheres and stability of the Reeb vector field ⋮ Area-minimizing vector fields on round 2-spheres ⋮ Unnamed Item ⋮ Harmonicity and minimality of oriented distributions ⋮ A critical radius for unit Hopf vector fields on spheres ⋮ Total curvature and volume of foliations on the sphere \(S^{2}\) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Stability of Left-Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups ⋮ Isoparametric functions, harmonic and minimal unit vector fields in K-contact geometry ⋮ Volume minimising unit vector fields on three dimensional space forms of positive curvature ⋮ Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.

Cites Work

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• On the volume of a unit vector field on the three-sphere
• Contact manifolds in Riemannian geometry
• 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 and harmonic characteristic vector fields on three-dimensional contact metric manifolds
• Linear invariants of Riemannian almost product manifolds
• Volumes of Vector Fields on Spheres
• Volumes of Flows
• Invariant minimal unit vector fields on Lie groups
• Harmonic and minimal radial vector fields
• Minimality and harmonicity for Hopf vector fields

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