Abstract
Twistor theory as we are going to see it was first developed by E. Calabi [25] in 1967. Other contributions were made—among others—by J. Eells and J. Wood in 1982 [34], F. Burstall and J. H. Rawnsley in 1986 [23], and K. Uhlenbeck in 1989 [82]. We are going to consider harmonic maps u: S2 → S n ⊂ ℝn+1, i. e. maps satisfying which is equivalent to Δu ∥ u. In contrast to Chapter 4, where we considered the Hopf differential we will also use derivatives of u of higher order. Let us first introduce some notations. We write
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