Skew Killing spinors

TL;DR

This paper investigates skew Killing spinors on 2 and 3-dimensional Riemannian spin manifolds, establishing their relation to twistor and parallel spinors through integrability conditions and conformal changes.

Contribution

It characterizes skew Killing spinors in low dimensions and links them to well-known spinor fields, providing new insights into their geometric properties.

Findings

Skew Killing spinors in 2D are equivalent to twistor spinors.

In 3D, they correspond to parallel spinors after a conformal change.

The paper derives integrability conditions for these spinors.

Abstract

In this paper, we study the existence of a skew Killing spinor (see the definition below) on 2 and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.