A generalisation of the Hopf Construction and harmonic morphisms into $\s^2$

S. Montaldo, A. Ratto

In this paper we construct a new family of harmonic morphisms $φ:V^5\to\s^2$, where $V^5$ is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of $\c^4=\r^8$.…