Harmonic morphisms on heaven spaces
Paul Baird, Radu Pantilie

TL;DR
This paper demonstrates that any analytic horizontally conformal submersion from a 3D conformal manifold to a 2D conformal manifold can be locally extended to a unique harmonic morphism from the associated heaven space.
Contribution
It establishes a unique extension of horizontally conformal submersions to harmonic morphisms on heaven spaces, linking conformal geometry with harmonic analysis.
Findings
Extension of conformal submersions to harmonic morphisms is unique.
Harmonic morphisms can be constructed from conformal submersions via heaven spaces.
The result applies to both real and complex analytic cases.
Abstract
We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold M to a two-dimensional conformal manifold N can be, locally, `extended' to a unique harmonic morphism from the heaven space of M to N.
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