The Minimal Polynomial of a Riemannian C_0-Space
Differential Geometry
2026-04-21 v2
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.
Keywords
Cite
@article{arxiv.2601.08827,
title = {The Minimal Polynomial of a Riemannian C_0-Space},
author = {Tillmann Jentsch},
journal= {arXiv preprint arXiv:2601.08827},
year = {2026}
}
Comments
The proof of Theorem 1.6 has been streamlined using the appropriate algebraic argument; the proof of Theorem 1.11 is now more concise. 24 pages