Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable
Lemaire, Luc ; Wood, John C.
Tohoku Math. J. (2), Tome 61 (2009) no. 1, p. 165-204 / Harvested from Project Euclid
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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.
Publié le : 2009-05-15
Classification:  Harmonic map,  Jacobi field,  infinitesimal deformation,  58E20,  53C43 
@article{1245849442,
     author = {Lemaire, Luc and Wood, John C.},
     title = {Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable},
     journal = {Tohoku Math. J. (2)},
     volume = {61},
     number = {1},
     year = {2009},
     pages = { 165-204},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245849442}
}

Lemaire, Luc; Wood, John C. Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable. Tohoku Math. J. (2), Tome 61 (2009) no. 1, pp.  165-204. http://gdmltest.u-ga.fr/item/1245849442/