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Construction of harmonic maps between pseudo-Riemannian spheres and hyperbolic spaces. (English) Zbl 0713.58009
Applying the Hopf-Whitehead construction to orthogonal multiplications gives rise to quadratic polynomial harmonic maps between spheres [cf. R. T. Smith, Harmonic maps of spheres, thesis, Warwick Univ. (1972), or the reviewer’s monograph ‘Harmonic maps and minimal immersions through representation theory’, Academic Press, Boston (1990; Zbl 0701.53002)]. The author generalizes this to the case when the underlying vector spaces for the orthogonal multiplication carry indefinite scalar products of various signatures and thereby obtains new examples of polynomial harmonic maps between pseudo-Riemannian space forms.
Reviewer: G.Tóth

MSC:
58E20 Harmonic maps, etc.
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