Talk:(G,X)-manifold

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 Field: Geometry

Introduction[edit]

We need a reference for the claim that the concept of a (G, X)-manifold generalizes all the various different types of manifolds, e.g. Riemannian manifolds, affine manifolds, piecewise linear manifolds, etc. It seems an unduly sweeping claim, especially the word "all". Deltahedron (talk) 09:12, 31 March 2013 (UTC)

This claim is not legitimate. (G, X)-structure are usually related to "flat" geometric structures. The notion you want to generalize Riemannian, ets. Manifolds is a Cartan geometry. (I rewrote the page so this comment no longer applies) jraimbau 14:35, 1 July 2016 (UTC) — Preceding unsigned comment added by Jean Raimbault (talkcontribs)

Complete rewrite[edit]

I rewrote the article, hopefully with a better presentation of the notion.

I added a section about the developing map (a fundamental notion) and some examples.

The page is far from being complete, some stuff that might be added:

  • Thurston's definition of a geometric manifold and the classification in dimension 3 (most important, likely I'll do it soon)
  • More examples and some developments about projective structures and their links to Teichmüller theory (possibly this could be done on a separate page)

jraimbau 14:31, 1 July 2016 (UTC) — Preceding unsigned comment added by Jean Raimbault (talkcontribs)