Talk:Flat manifold

The sentence "Bieberbach's theorem states that all compact flat manifolds are tori." is flatly wrong. For example, the Klein bottle admits a flat metric, is compact, and is not a torus. I'll try to find a book that contains the correct statement -- it seems hard to find online! best, Sam nead (talk) 01:50, 25 January 2009 (UTC)[reply]

Fixed. Sam nead (talk) 02:02, 25 January 2009 (UTC)[reply]

The projective plane is not a flat manifold. best, Sam nead (talk) 23:31, 2 February 2009 (UTC)[reply]

Needs work to be much clearer[edit]

The article sometimes discusses distinct flat metrics on manifolds, and at other times ("There are 10 compact flat 3-manifolds") discusses topology.

It is important for the article to state what it is talking about. I hope someone knowledgeable about this subject can fix the many places where this article is unclear. 2601:200:C082:2EA0:3CCE:4C0A:EE79:3CF3 (talk) 15:02, 5 August 2023 (UTC)[reply]