New Minimal Surfaces of the Sphere and the Hyperbolic Space via Harmonic Morphisms
arXiv:2603.24301
summary
The paper presents a new method using complex-valued harmonic morphisms to construct explicit minimal codimension‑two submanifolds in the 4‑sphere and 4‑dimensional hyperbolic space.
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 and the hyperbolic space .
Topics & keywords
#minimal surfaces#harmonic morphisms#spherical geometry#hyperbolic geometry#submanifoldsminimal submanifoldscodimension twocomplex-valued harmonic morphismsS^4H^4explicit examples