Harmonic vector fields on extended 3-dimensional Riemannian Lie groups

2020/09/25 by Ferdinand Hountondji Koudjo, Koudjo, Ferdinand Hountondji, E. Loubeau +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2009.13296

openalex publication_date 2020/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given two Riemannian manifolds (B,g_B) and (F,g_F), we give harmonicity conditions for vector fields on the Riemannian warped product B×_fF, with f:B \longrightarrow ]0,+∞[, using a characteristic variational condition. Then, we apply this to the case B=ℝ and F is a three-dimensional connected Riemannian Lie group G equipped with a left-invariant metric, to determine harmonic vector fields on ℝ×_fG. We give examples of harmonic vector fields on G which are not left-invariant and determine harmonic vector fields on ℝ×_fG. We conclude with some examples of vector fields on ℝ×_fG which are harmonic maps.

Citations

• Harmonic Mappings of Riemannian Manifolds

Related

• Harmonic Vector Fields on Space Forms
• Higher-power harmonic maps and sections
• Harmonic maps into sub-Riemannian Lie groups
• On the Interpolating Sesqui-Harmonicity of Vector Fields
• Harmonic vector fields on pseudo-Riemannian manifolds