# A generalisation of the Hopf construction and harmonic morphisms into $${\mathbb {S}^2}$$

@article{Montaldo2010AGO,
title={A generalisation of the Hopf construction and harmonic morphisms into \$\$\{\mathbb \{S\}^2\}\$\$},
author={Stefano Montaldo and Andrea Picasso Ratto},
journal={Annali di Matematica Pura ed Applicata},
year={2010},
volume={189},
pages={605-613}
}
In this paper, we construct a new family of harmonic morphisms $${\varphi:V^5\to\mathbb{S}^2}$$, where V5 is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of $${\mathbb{C}^4\,=\,\mathbb{R}^8}$$. These harmonic morphisms admit a continuous extension to the completion $${{V^{\ast}}^5}$$, 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.