Harmonic maps from S² to HP²

Le résumé fourni par la source

In this paper, we describe all harmonic maps from the Riemann 2-sphere to HP 2 y the quaternion 2-projective space.In example 1.3, all isotropic harmonic maps from S 2 to HP n are given.A particular class of nonisotropic harmonic maps from S 2 to HP n are classified by Theorem 1.4.With theorem 1.5, the description of harmonic maps from *S 2 to HP 2 becomes complete.Harmonic maps from S 2 to S n and S 2 to CP n are classified by Calabi.E [1] and Eells-Wood [2] respectively.Our description of harmonic maps from *S 2 to HP 2 is not as elegant as those of Calabi and Eells-Wood.Still it gives hope for classifying harmonic maps from S 2 to compact symmetric spaces.We state our main results in §1.§2 contains some preliminaries.In §3, the proof of theorem 1.4 is given.Theorem 1.5 is proved in §4.Here we use some of the ideas from [6].I am grateful to M.V. Nori for suggesting the problem and also for many useful discussions.

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