Normal Conformal Killing Forms

TL;DR

This paper introduces normal twistor equations for differential forms, studies their solutions called normal conformal Killing forms, and explores their relation to conformal geometry, holonomy reductions, and Lorentzian spin manifolds.

Contribution

It develops a new framework for normal twistor equations in conformal geometry and analyzes their solutions in relation to holonomy and spinor fields.

Findings

Normal conformal Killing forms are characterized via twistor equations.

Holonomy reductions correspond to special solutions of these equations.

Applications to Lorentzian spin manifolds with conformal Killing spinors.

Abstract

We introduce in this paper normal twistor equations for differential forms and study their solutions, the so-called normal conformal Killing forms. The twistor equations arise naturally from the canonical normal Cartan connection of conformal geometry. Reductions of its holonomy are related to solutions of the normal twistor equations. The case of decomposable normal conformal holonomy representations is discussed. A typical example with an irreducible holonomy representation are the so-called Fefferman spaces. We also apply our results to describe the geometry of solutions with conformal Killing spinors on Lorentzian spin manifolds.