Talk:Hilbert's theorem (differential geometry)
 | This article is rated B-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
| |||||||||||
Missing ingredient in statement and proof of theorem
[edit]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)