Jump to content

Talk:Flat manifold

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia

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]