Talk:Conformally flat manifold

Yamabe problem
I'm not sure, but the Yamabe problem seems to say that *every* Rieman manifold is conformally equivalent to one of constant scalar curvature. This seems not to hold for pseudo-Riemannian manifolds; and its unclear to me whether or how "can be made flat locally" is promoted to a global statement. That is, are there manifolds which can everywhere be made flat locally, but can't be made such globally? (viz some kind of combing-of-hair type theorem?) 67.198.37.17 (talk) 04:51, 1 May 2019 (UTC)