New Minimal Surfaces of the Sphere $S^4$ and the Hyperbolic Space $H^4$ via Harmonic Morphisms

Abstract

In this work we introduce a new method for the construction of minimal submanifolds of codimension two in even dimensional spheres and hyperbolic spaces. This is based on the theory of complex-valued harmonic morphisms. This gives the first explicit examples of such maps defined on the sphere $S^4$ and the hyperbolic space $H^4$.