Killing-Yano Tensors of Order n-1

TL;DR

This paper investigates Killing-Yano tensors of order n-1 in n-dimensional manifolds, deriving integrability conditions, classifying metrics that admit them, and exploring their connection to generalized angular momentum.

Contribution

It provides a complete classification of metrics with Killing-Yano tensors of order n-1 and introduces a method to generate conformal Killing vectors using manifold symmetries.

Findings

All metrics admitting such tensors are characterized.

A connection between these tensors and generalized angular momentum is established.

A theorem for generating closed conformal Killing vectors is proved.

Abstract

The properties of a Killing-Yano tensor of order n-1 in an n-dimensional manifold are investigated. The integrability conditions are worked out and all metrics admitting a Killing-Yano tensor of order n-1 are found. It is pointed out a connection between such tensors and a generalization of the concept of angular momentum. A theorem on how to generate closed conformal Killing vectors using the symmetries of a manifold is proved and used to find all Killing-Yano tensors of order n-1 of a maximally symmetric space.