The identity map as a harmonic map of a \((4r+3)\)-sphere with deformed metrics
type: Item
instance of: scholarly article
title: The identity map as a harmonic map of a \((4r+3)\)-sphere with deformed metrics
zbMATH Open document ID: 0808.53042
author: Shukichi Tanno
published in: Kodai Mathematical Journal
publication date: 1995-03-16T00:00:00Z
review text: The author studies the instability of the sphere \(S^{4n + 3}\) with metrics \(g(t)\) obtained by specific deformation relative to the Hopf \(S^ 3\)-fibration of \(S^{4n + 3}\). Here instability means that the energy of the identity map has second variation with negative eigenvalues. The corresponding problem relative to the Hopf \(S^ 1\)- fibration of \(S^{2n + 1}\) was treated in [\textit{S. Tanno}, Kodai Math. J. 10, 250-257 (1987; Zbl 0629.53043)].
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 515589
zbMATH Keywords: identity map
zbMATH Keywords: harmonic instability
zbMATH Keywords: Hopf fibration
reviewed by: J. Eells
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039781
OpenAlex ID: W1980631048
cites work: Q3658778
cites work: On the stability of a three-sphere
cites work: Q4745012
cites work: Stability of harmonic maps and standard minimal immersions
cites work: The Second Variation Formula for Harmonic Mappings
cites work: The first eigenvalue of the Laplacian on spheres
cites work: Some metrics on a (4r+3)-sphere and spectra
cites work: Some functions on the set of triangles or quadrangles
cites work: Instability of spheres with deformed Riemannian metrics
cites work: On the least positive eigenvalue of the Laplacian for compact group manifolds
cites work: Q4722777
cites work: Stability of Harmonic Maps and Eigenvalues of the Laplacian
cites work: Some results on stable harmonic maps
DOI: 10.2996/KMJ/1138039781
description: scientific article; zbMATH DE number 515589