Moduli spaces for finite-order jets of Riemannian metrics

Understand

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold.

• The construction is closely related to the problem of classification of jet metrics via differential invariants.
• The moduli space is proved to be a differentiable space which admits a finite canonical stratification into smooth manifolds.
• A complete study on the stratification of moduli spaces is carried out for metrics in dimension n=2.