By Caramba

2012-10-15 02:29:21 8 Comments

This is quite well-known: the ONLY metric invariants are curvature, its higher derivatives, and any possible contractions between them.

The meaning of an invariant is, to put it simply, a tensor that is decided by the metric in a "canonical" way, but is independent on local coordinates.

So my question is how such a result is proved?


@Peter Michor 2012-10-15 08:01:26

See section 33 of the book: Ivan Kolár, Jan Slovák, Peter W. Michor: Natural operations in differential geometry. Springer-Verlag, Berlin, Heidelberg, New York, (1993), (pdf).