Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion

TL;DR

This paper derives integrability conditions for Killing-Yano tensors with torsion, classifies compatible metrics and torsions, and explores the concept of maximally symmetric spaces in torsionful geometries.

Contribution

It provides the first comprehensive analysis of Killing-Yano tensors in spaces with torsion and defines maximally symmetric spaces under torsionful connections.

Findings

Derived integrability conditions for Killing-Yano tensors with torsion

Classified metrics and torsions compatible with Killing-Yano tensors

Addressed the definition of maximally symmetric spaces with torsion

Abstract

The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order n-1 are obtained. Finally, the issue of defining a maximally symmetric space with respect to connections with torsion is addressed.