Talk:Conformal geometry

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[edit] Conformally flat geometry

There are a couple of serious ommissions here. Not all flat conformal Riemannian geometry has to do with the geometry of spheres. For instance, consider the conformal geometry consisting of hyperbolic transformations of the Poincaré disc to itself (also, confusingly, called Möbius transformations). In higher dimensions, one can talk about conformal transformations of the ball to itself. Of course, for curved conformal geometry it is the sphere model which turns out to be most useful. Personally, I advocate exporting most of this to another article: Möbius geometry for the Euclidean case and (I'm not really sure what) for the Lorentzian case. Silly rabbit 19:39, 12 November 2005 (UTC)