Irreducible Killing Tensors from Third Rank Killing-Yano Tensors

TL;DR

This paper explores the construction of irreducible Killing tensors from third rank Killing-Yano tensors, demonstrating their non-triviality through explicit examples and expanding understanding of symmetries in differential geometry.

Contribution

It shows that third rank Killing-Yano tensors can generate irreducible Killing tensors, providing explicit examples with the Kimura IIC metric.

Findings

Third rank Killing-Yano tensors can produce irreducible Killing tensors.

Explicit example with Kimura IIC metric demonstrates the construction.

Two irreducible and one reducible Killing tensor obtained from third rank tensors.

Abstract

We investigate higher rank Killing-Yano tensors showing that third rank Killing-Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric were from two rank Killing-Yano tensors we obtain a reducible Killing tensor and from third rank Killing-Yano tensors we obtain three Killing tensors, one reducible and two irreducible.