A characterization of Dirac morphisms

TL;DR

This paper characterizes Dirac morphisms, which are maps that preserve harmonic spinor fields under pullback, by relating Dirac operators on total and base manifolds of horizontally conformal submersions.

Contribution

It provides a new characterization of Dirac morphisms through the relationship between Dirac operators on total and base spaces.

Findings

Identifies conditions under which a map is a Dirac morphism

Establishes a link between harmonic spinor fields and submersion geometry

Provides a framework for analyzing Dirac operators in fibered spaces

Abstract

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.