Harmonic Morphisms from Minkowski Space and Hyperbolic Numbers
نویسندگان
چکیده
We show that all harmonic morphisms from 3-dimensional Minkowski space with values in a surface have a Weierstrass representation involving the complex numbers or the hyperbolic numbers depending on the signature of the codomain. We deduce that there is a nontrivial globally defined submersive harmonic morphism from Minkowski 3-space to a surface, in contrast to the Riemannian case. We show that a degenerate harmonic morphism on a Minkowski space is precisely a null real-valued solution to the wave equation, and we find all such.
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