Higher-power harmonic maps and sections

Christopher Malcolm Wood; Anand Ramachandran

Higher-power harmonic maps and sections

Christopher Malcolm Wood, Anand Ramachandran

Mathematics

Research output: Working paper › Preprint

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
Publisher	arXiv
Number of pages	32
Publication status	Published - 11 Feb 2019

Keywords

Higher-power energy, higher-power harmonic map, r-conformal map, higher-power harmonic section, r-horizontal section, Newton tensor, twisted skyrmion, Riemannian vector bundle, r-parallel section, sphere subbundle, 3-dimensional unimodular Lie group, left-invariant metric, invariant (unit) vector field, Milnor map, principal Ricci/sectional curvature.

Access to Document

https://arxiv.org/abs/1902.03134Licence: Unspecified

Cite this

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

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keywords = "Higher-power energy, higher-power harmonic map, r-conformal map, higher-power harmonic section, r-horizontal section, Newton tensor, twisted skyrmion, Riemannian vector bundle, r-parallel section, sphere subbundle, 3-dimensional unimodular Lie group, left-invariant metric, invariant (unit) vector field, Milnor map, principal Ricci/sectional curvature.",

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