In this paper, we construct a new family of harmonic morphisms φ : V^5 → S^2, where V^5 is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of C^4 = R^8. These harmonic morphisms admit a continuous extension to the completion V∗^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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