Moduli spaces for finite-order jets of Riemannian metrics
arXiv:0808.2996 · doi:10.1016/j.difgeo.2010.07.002
Abstract
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.
25 pages, corrected typos, partially changed content with an appendix added