Harmonic 2-spheres with 𝑟 pairs of extra eigenfunctions

Kotani, Motoko

doi:10.1090/S0002-9939-97-03771-4

Harmonic 2-spheres with $r$ pairs of extra eigenfunctions
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Proc. Amer. Math. Soc. 125 (1997), 2083-2092 Request permission

Abstract:

In the present paper, deformations of harmonic 2-spheres in the unit $n$-sphere $S^{n}$ respecting the degree are studied. The limit maps of such deformations are characterized as harmonic maps with extra eigenfunctions. The space $Harm_{d}(S^{2},S^{n})$ of harmonic 2-spheres in $S^{n}$ with fixed degree $d$ is described in terms of such deformations and the limit maps.

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