A generalisation of the Hopf construction and harmonic morphisms into {mathbb {S}^2} |
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| Authors: | S. Montaldo A. Ratto |
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| Affiliation: | 1. Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy
2. Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Viale Merello 93, 09123, Cagliari, Italy
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| Abstract: | In this paper, we construct a new family of harmonic morphisms ${varphi:V^5tomathbb{S}^2}In this paper, we construct a new family of harmonic morphisms j:V5?mathbbS2{varphi:V^5tomathbb{S}^2}, where V 5 is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of mathbbC4 = mathbbR8{mathbb{C}^4,=,mathbb{R}^8}. These harmonic morphisms admit a continuous extension to the completion V*5{{V^{ast}}^5}, which turns out to be an explicit real algebraic variety. We work in the context of a generalization of the Hopf construction and equivariant theory. |
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