Higher-power harmonic maps and sections

Chris Wood; Anand Ramachandran

doi:10.1007/s10455-022-09875-9

Higher-power harmonic maps and sections

Chris Wood^*, Anand Ramachandran

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	6
Number of pages	43
Journal	Annals of Global Analysis and Geometry
Volume	63
DOIs	https://doi.org/10.1007/s10455-022-09875-9
Publication status	Published - 7 Nov 2022

Bibliographical note

Keywords

Higher-power energy, higher-power harmonic maps, minimal immersion, $r$-conformal map, higher-power harmonic sections, $r$-horizontal section, Newton polynomials, Newton's identities, Newton tensor, curvature of a submersion, twisted skyrmion, Riemannian vector bundle, $r$-parallel section, sphere subbundle, Hopf map, $3$-dimensional unimodular Lie group, left-invariant metric, invariant (unit) vector field, Milnor map, principal Ricci curvatures

Access to Document

10.1007/s10455-022-09875-9Licence: CC BY

s10455-022-09875-9
© The Author(s) 2022
Final published version, 637 KBLicence: CC BY

Cite this

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title = "Higher-power harmonic maps and sections",

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.",

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AU - Ramachandran, Anand

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