Higher-power harmonic maps and sections

2019/02/08 by A. Ramachandran, Ramachandran, A., C. M. Wood +1
Mathematics · Physics and Astronomy · #53C05 #53C43 #58E20 #58E30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.1902.03134

openalex publication_date 2019/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The variational theory of higher-power energy is developed for mappings between Riemannian manifolds, and more generally sections of submersions of Riemannian manifolds, and applied to sections of Riemannian vector bundles and their sphere subbundles. A complete classification is then given for left-invariant vector fields on 3-dimensional unimodular Lie groups equipped with an arbitrary left-invariant Riemannian metric.

Related

• Harmonic vector fields on extended 3-dimensional Riemannian Lie groups
• Harmonicity of sections of sphere bundles
• The second variational formula of the k-energy and k-harmonic curves
• Harmonic maps into sub-Riemannian Lie groups
• Tangent bundles to sub-Riemannian groups