Harmonic morphisms on heaven spaces

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.

9 pages

References in corpus (2)

• Selfdual Einstein metrics and conformal submersions
• Harmonic morphisms between Weyl spaces and twistorial maps II

Cited by in corpus (3)

• CR geometry and conformal foliations
• Generalized Quaternionic Manifolds
• On Ricci solitons and twistorial harmonic morphisms