Invariant harmonic unit vector fields on the oscillator groups

DOI10.21136/CMJ.2019.0538-17MaRDI QIDQ5206446

Na Xu, Ju Tan

Publication date: 18 December 2019

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

harmonic mapharmonic vector fieldoscillator group

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Differential geometric aspects of harmonic maps (53C43)

Cites Work

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• Harmonicity of vector fields on four-dimensional generalized symmetric spaces
• Examples of algebraic Ricci solitons in the pseudo-Riemannian case
• Solutions of the Yang-Baxter equations on quadratic Lie groups: the case of oscillator groups
• Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
• Chronogeometry of an electromagnetic wave given by a bi-invariant metric on the oscillator group
• Curvatures of left invariant metrics on Lie groups
• Relationship between volume and energy of vector fields.
• 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
• Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.
• Total bending of vector fields on Riemannian manifolds
• Homogeneous Lorentzian structures on the oscillator groups
• Reductive decompositions and Einstein–Yang–Mills equations associated to the oscillator group
• Harmonic and minimal radial vector fields
• Minimality and harmonicity for Hopf vector fields

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