Jacobi Fields along Harmonic 2 - Spheres in S 3 and S 4 Are Not All Integrable
نویسنده
چکیده
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 a smooth 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 4sphere 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.
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0 Se p 20 07 JACOBI FIELDS ALONG HARMONIC 2 - SPHERES IN S 3 AND S 4 ARE NOT ALL INTEGRABLE
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 a smooth 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 4sphere which have non-integrable Jacobi fields. This is particularly surprising ...
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