Talk:Hilbert's theorem (differential geometry)

Missing ingredient in statement and proof of theorem

Hilbert's theorem excludes only immersions that are at least of differentiability class C². This is in fact *false* for differentiability class C¹ -- there exist, e.g., C¹ isometric embeddings of the hyperbolic plane in R³ (see the theorem of Nash-Kuiper).

The statement of Hilbert's theorem, therefore, ought to mention that this theorem holds only for differentiability class at least C² -- and the proof ought to state where this is relevant.Daqu (talk) 18:17, 18 July 2008 (UTC)