On nonrigidity of harmonic maps into spheres

Tóth, Gábor

doi:10.1090/S0002-9939-1985-0792288-4

On nonrigidity of harmonic maps into spheres
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Proc. Amer. Math. Soc. 94 (1985), 711-714 Request permission

Abstract:

This note studies nonrigidity of equivariant harmonic maps $f:M \to {S^n}$ of a Riemannian homogeneous space $M$ into the Euclidean $n$-sphere ${S^n}$ via representation theory applied to the induced module structure on ${{\mathbf {R}}^n}$ and, for specific $M$, produces (divergence-free) Jacobi fields along $f$ which do not come from isometric deformations of $f$ on the range.

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