The number of functionally independent invariants of a pseudo--Riemannian metric

TL;DR

This paper determines the count of functionally independent scalar invariants of any order for a generic pseudo-Riemannian metric on an n-dimensional manifold, providing a comprehensive understanding of their structure.

Contribution

It explicitly calculates the number of independent invariants of arbitrary order for generic pseudo-Riemannian metrics, advancing the classification of such metrics.

Findings

Number of invariants depends on the dimension n and the order of derivatives.

Provides a formula for the count of independent invariants.

Enhances understanding of geometric invariants in pseudo-Riemannian geometry.

Abstract

The number of functionally independent scalar invariants of arbitrary order of a generic pseudo--Riemannian metric on an $n$--dimensional manifold is determined.