The Minimal Polynomial of a Riemannian C_0-Space

TL;DR

This paper introduces a polynomial invariant at each point of a Riemannian C_0-space, which can be globally assembled in homogeneous cases and relates to the Singer invariant.

Contribution

It constructs a pointwise polynomial invariant with polynomial coefficients that are Killing tensors, linking to the Singer invariant in homogeneous Riemannian C_0-spaces.

Findings

Constructs pointwise polynomials with polynomial coefficients on tangent spaces.

These polynomials glue into a global invariant in homogeneous spaces.

The polynomial degree bounds the Singer invariant of the space.

Abstract

We construct, at each point of a Riemannian C_0-space, a polynomial in one variable whose coefficients are polynomial functions on the tangent space. For a homogeneous Riemannian C_0-space (for instance, a G.O. space) these pointwise-defined polynomials glue together to a global polynomial whose coefficients are Killing tensors invariant under the full isometry group. Moreover, the degree of this polynomial provides an upper bound for the Singer invariant of the space.