Abstract
In a previous paper, we showed that any Jacobi field along a harmonic map from the 2-sphere to the complex projective plane is integrable (i.e., is tangent to asmooth variation through harmonic maps). In this paper, in contrast, we show that there are (non-full) harmonic maps from the 2-sphere to the 3-sphere and 4-sphere which have non-integrable Jacobi fields. This is particularly surprising in the case of the 3-sphere where the space of harmonic maps of any degree is a smooth manifold, each map having image in a totally geodesic 2-sphere.
Citation
Luc Lemaire. John C. Wood. "Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable." Tohoku Math. J. (2) 61 (2) 165 - 204, 2009. https://doi.org/10.2748/tmj/1245849442
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