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Harmonic Morphisms and Bicomplex Manifolds by Baird, Paul; Wood, John C. is a scholarly article available to read on EtoBox.

What is Harmonic Morphisms and Bicomplex Manifolds about?

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.

Author

Baird, Paul; Wood, John C.

Published

2009

Language

EN