Harmonic maps from spheres to spheres
type: Item
instance of: scholarly article
title: Harmonic maps from spheres to spheres
zbMATH Open document ID: 0889.55007
DOI: 10.1016/S0040-9383(96)00050-X
author: Zizhou Tang
author: Chiakuei Peng
published in: Topology
publication date: 1998-06-18T00:00:00Z
review text: The authors give new examples of elements from the homotopy groups of spheres which are harmonically representable. If \(p,q\geq 3\), one knows that every orthogonal multiplication \(g:\mathbb{R}^p \times \mathbb{R}^q \to \mathbb{R}^n\) gives rise, via the Hopf construction on the associated map, \(S^{p-1} \times S^{q-1} \to S^{n-1}\) to a map \(f:S^{p+ q-1} \to S^n\), which has a harmonic representative by the Ratto-Ding theorem [\textit{W.-Y. Ding}, Int. J. Math. 5, No. 6, 849-860 (1994; Zbl 0822.58011)]. The main results concern the precise description of \([f]\in \pi_{p+ q-1}S^n\), for various particular choices of \(g\).
Mathematics Subject Classification ID: 55Q40
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1089982
zbMATH Keywords: homotopy groups of spheres
zbMATH Keywords: harmonic maps
zbMATH Keywords: harmonic representatives
reviewed by: Ştefan Papadima
MaRDI profile type: Publication
full work available at URL: s0040-9383(96)00050-x
OpenAlex ID: W1982600247
description: scientific article; zbMATH DE number 1089982