Spinor bilinears and Killing-Yano forms in generalized geometry

TL;DR

This paper explores the properties of spinor bilinears and Killing-Yano forms within generalized geometry, establishing their relationships and constructing new forms using generalized Killing spinors.

Contribution

It introduces a framework connecting spinor bilinears with Killing-Yano forms in generalized geometry, extending classical concepts to a broader geometric setting.

Findings

Killing equation expressed via generalized covariant derivative

Construction methods for generalized Killing-Yano forms

Relations between spinor bilinears and differential forms

Abstract

Spinor bilinears of generalized spinors and their properties are investigated. Generalized Killing and twistor spinor equations are considered and their relations to the equations satisfied by special types of differential forms are found. Killing equation in generalized geometry is written in terms of the generalized covariant derivative and Killing-Yano forms are described in the framework of generalized geometry. Construction of generalized Killing-Yano forms and generalized closed conformal Killing-Yano forms in terms of the spinor bilinears of generalized Killing spinors are determined.