Weierstrass representations for harmonic morphisms on Euclidean spaces and spheres
P. Baird (Brest), J.C. Wood (Leeds)
TL;DR
This paper develops Weierstrass-type representations to construct extensive families of harmonic morphisms that are holomorphic relative to Hermitian structures, leading to new examples on Euclidean spaces and spheres.
Contribution
It introduces hierarchies of Weierstrass-type representations to generate harmonic morphisms, expanding the known classes on Euclidean spaces and spheres.
Findings
Constructed large families of harmonic morphisms
Found new examples on Euclidean spaces
Found new examples on spheres
Abstract
We construct large families of harmonic morphisms which are holomorphic with respect to Hermitian structures by finding heierarchies of Weierstrass-type representations. This enables us to find new examples of complex-valued harmonic morphisms from Euclidean spaces and spheres.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Geometry and complex manifolds