Harmonic vector fields on extended 3-dimensional Riemannian Lie groups

zbMath1497.58010arXiv2009.13296MaRDI QIDQ5867395

Leonard Todjihounde, Ferdinand Hountondji Koudjo, Eric Loubeau

Publication date: 14 September 2022

Full work available at URL: https://arxiv.org/abs/2009.13296

zbMATH Keywords

harmonic mapstangent sphere bundlewarped productsharmonic vector fieldsthree dimensional Riemannian Lie groups

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Harmonic maps, etc. (58E20)

Cites Work

• The bienergy of unit vector fields
• Harmonicity properties of invariant vector fields on three-dimensional Lorentzian Lie groups
• Curvatures of left invariant metrics on Lie groups
• Unit vector fields on spheres, which are harmonic maps
• Relationship between volume and energy of vector fields.
• Total bending of vector fields on Riemannian manifolds
• The Gauss Section of a Riemannian Immersion
• Harmonic Mappings of Riemannian Manifolds
• On the energy of a unit vector field
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