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arXiv · 2603.24301

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

Sigmundur Gudmundsson·Leonard Nygren Löhndorf
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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 $H^4$.

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Sigmundur Gudmundsson, Leonard Nygren Löhndorf. 2026-03-25. New Minimal Surfaces of the Sphere $S^4$ and the Hyperbolic Space $H^4$ via Harmonic Morphisms. https://arxiv.org/abs/2603.24301

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