\(Sp(n)\)-equivariant harmonic maps between complex projective spaces
type: Item
instance of: scholarly article
title: \(Sp(n)\)-equivariant harmonic maps between complex projective spaces
zbMATH Open document ID: 0918.58021
author: Toshimasa Kobayashi
published in: Tsukuba Journal of Mathematics
publication date: 1999-08-04T00:00:00Z
review text: The author studies the existence and harmonicity of \(Sp(n)\)-equivariant maps between complex projective spaces by using the fact that the symplectic group \(Sp(n)\) acts on a \((2n-1)\)-dimensional complex projective space \(\mathbb{C} P^{2n-1}\) transitively. All complex irreducible representations of \(Sp(n)\) which define \(Sp(n)\)-equivariant maps from \(\mathbb{C} P^{2n-1}\) to \(\mathbb{C} P^m\) are determined. The author proves that the associated \(Sp(n)\)-equivariant maps are harmonic for any \(Sp(n)\)-invariant Riemannian metric on \(\mathbb{C} P^{2n-1}\). He obtains \(Sp(n)\)-equivariant minimal immersions from \(\mathbb{C} P^{2n-1}\) to \(\mathbb{C} P^m\), but not \(SU(2n)\)-equivariant ones.
reviewed by: Chandra Shekhar Sharma
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 19L47
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 1102803
zbMATH Keywords: equivariance
zbMATH Keywords: harmonic maps
zbMATH Keywords: projective spaces
zbMATH Keywords: Grassmannian manifolds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162983
OpenAlex ID: W2143996301
DOI: 10.21099/TKBJM/1496162983
description: scientific article; zbMATH DE number 1102803