Weierstrass representations for harmonic morphisms on Euclidean spaces and spheres

1995/12/20 by P. Baird, J. C. Wood, Baird, P. +1
Mathematics · #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG #msc:58E20

paper · pdf · doi:10.48550/arxiv.dg-ga/9512010

Minor revision adding example. Latex 2.09. 14 pages

arxiv created 1996/05/24 · arxiv updated 2009/11/30

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.

Related

• Hermitian structures and harmonic morphisms in higher dimensional Euclidean spaces
• Harmonic spheres in outer symmetric spaces, their canonical elements and Weierstrass type representations
• Complete lifts of harmonic maps and morphisms between Euclidean spaces
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• Harmonic morphisms from homogeneous Hadamard manifolds