Minimal unit vector fields with respect to Riemannian natural metrics

DOI10.1016/J.DIFGEO.2013.09.005zbMath1484.53068OpenAlexW2057795353WikidataQ115356499 ScholiaQ115356499MaRDI QIDQ386024

Domenico Perrone

Publication date: 13 December 2013

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

Full work available at URL: https://doi.org/10.1016/j.difgeo.2013.09.005

zbMATH Keywords

critical pointsminimal submanifoldsKilling vector fieldsReeb vector fieldsHopf vector fieldsminimal vector fieldsRiemannian natural metricsvolume 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) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items (3)

Bochner flatness of tangent bundles with \(g\)-natural almost Hermitian metrics ⋮ Geometry of a surface in Riemannian 3-manifold corresponding to a smooth autonomous dynamical system ⋮ Unit vector fields of minimum energy on quotients of spheres and stability of the Reeb vector field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometry of Kaluza-Klein metrics on the sphere \(\mathbb S^3\)
• Harmonic maps and Kaluza-Klein metrics on spheres
• Harmonic morphisms and Riemannian geometry of tangent bundles
• Stability of the Reeb vector field of \(H\)-contact manifolds
• Unit vector fields on real space forms which are harmonic maps
• Naturality of homogeneous metrics on stiefel manifolds \(SO(m + 1)/SO(m - 1)\)
• Stability of unit Hopf vector fields on quotients of spheres
• Harmonicity of unit vector fields with respect to Riemannian \(g\)-natural metrics
• On some real hypersurfaces of a complex hyperbolic space
• On the volume of a unit vector field on the three-sphere
• CR submanifolds of Kaehlerian and Sasakian manifolds
• Real hypersurfaces in a complex projective space with constant principal curvatures
• Criticality of K-contact vector fields
• Minimal unit vector fields
• On some hereditary properties of Riemannian \(g\)-natural metrics on tangent bundles of Riemannian manifolds
• HARMONIC SECTIONS OF TANGENT BUNDLES EQUIPPED WITH RIEMANNIAN g-NATURAL METRICS
• MINIMALITY, HARMONICITY AND CR GEOMETRY FOR REEB VECTOR FIELDS
• Volumes of Flows
• Riemannian geometry of contact and symplectic manifolds
• Invariant minimal unit vector fields on Lie groups
• Minimality and harmonicity for Hopf vector fields

This page was built for publication: Minimal unit vector fields with respect to Riemannian natural metrics