Harmonic morphisms and bicomplex manifolds

  • Baird P
  • Wood J
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Abstract

We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of complex-harmonic morphism between complex-Riemannian manifolds and showing how these are given by bicomplex-holomorphic functions when the codomain is one-bicomplex dimensional. By taking real slices, we recover well-known compactifications for the three possible real cases. On the way, we discuss some interesting conformal compactifications of complex-Riemannian manifolds by interpreting them as bicomplex manifolds. © 2010 Elsevier B.V.

Author-supplied keywords

  • Bicomplex number
  • Harmonic map
  • Harmonic morphism

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Authors

  • Paul Baird

  • John C. Wood

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