Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable

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概要

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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.

• 東北大学の論文

著者

• Lemaire Luc

  Department De Mathematique Universite Libre De Bruxelles

• Wood John

  Department Of Pure Mathematics University Of Leeds

• Wood John

  Department Of Molecular And Integrative Physiology University Of Kansas Medical Center

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• Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable
• JACOBI FIELDS ALONG HARMONIC 2-SPHERES IN 3- AND 4-SPHERES ARE NOT ALL INTEGRABLE

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