A generalisation of the Hopf Construction and harmonic morphisms into ²

الأصل · EN

In this paper we construct a new family of harmonic morphisms φ:V⁵→², where V⁵ is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of ⁴=⁸. These harmonic morphisms admit a continuous extension to the completion V⁵, 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.