Conformally Invariant Spinorial Equations in Six Dimensions

TL;DR

This paper explores conformally invariant spinorial equations in six dimensions, deriving their geometric interpretations, integrability conditions, and related curvature identities, advancing understanding of massless fields and harmonic forms in higher-dimensional geometry.

Contribution

It introduces new conformally invariant spinorial equations in six dimensions and analyzes their geometric and integrability properties, providing foundational insights for higher-dimensional conformal geometry.

Findings

Derived several conformally invariant equations in six-dimensional spinorial formalism.

Established integrability conditions for these equations.

Obtained useful curvature identities related to the spinorial connection.

Abstract

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, some useful identities involving the curvature of the spinorial connection are attained and a digression about harmonic forms and more general massless fields is made.