An estimate for the Singer invariant via the Jet Isomorphism Theorem

TL;DR

This paper computes the Singer invariants of certain Riemannian homogeneous spaces with linear Jacobi relations using computer algebra, and discusses these results through the Jet Isomorphism Theorem.

Contribution

It introduces a method to estimate the Singer invariant for specific spaces utilizing the Jet Isomorphism Theorem and computer algebra tools.

Findings

Computed Singer invariants for new homogeneous spaces

Demonstrated the application of the Jet Isomorphism Theorem in this context

Provided insights into the structure of spaces with linear Jacobi relations

Abstract

Recently examples of Riemannian homogeneous spaces with linear Jacobi relations were found. We calculate the Singer invariants of these spaces with the computer algebra program Maple and discuss the results by means of the Jet Isomorphism Theorem of pseudo-Riemannian geometry.