Talk:Two-dimensional space

Previous discussion
Can be found at. fgnievinski (talk) 04:34, 22 December 2023 (UTC)

Riemann surfaces
Should the article mention Riemann surfaces as a special case? Note that while they are of dimension 2 as real surfaces they are of dimension 1 as complex spaces. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:04, 26 December 2023 (UTC)


 * Sure, why not? Maybe Lorentz surfaces as well at the same time. We may want to also mention Lorentzian and symplectic surfaces somewhere.
 * While we're at it we should probably have some article about the generalization to arbitrary metric signature of 2-dimensional space forms, maybe titled non-Euclidean plane or something (I'm not sure if there's a standard name in the literature, but currently our only article is Cayley–Klein metric which isn't really the right scope for this), including not just the 2-sphere, Euclidean plane, and hyperbolic plane but also the the Galilean plane, Lorentzian plane, de Sitter plane, Anti-de Sitter plane, and the duals of the Euclidean plane and Lorentzian plane (not sure what the best or most common name is for these), all of which should also have their own separate articles. –jacobolus (t) 21:21, 26 December 2023 (UTC)


 * @Chatul I made some additions. Is that helpful? (Feel free to make further changes.) –jacobolus (t) 01:40, 27 December 2023 (UTC)


 * Perfect. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 15:58, 27 December 2023 (UTC)

Scope of article?
In physics, there's an assortment of exactly solvable models that are 2D, including assorted wave phenomena, ergodic mixing of energy eigenmodes, solitons, etc. That, plus a lot of semiconductor stuff happens at 2D interfaces, including some high-temp superconductors. Anyone care to broaden the scope of this article to "all things math-physical in 2D"? Or should there be some cutoff criteria, like "this will only be about math, dagnabit."? I don't want to expand the boundaries to biological cell membranes, even though I recently stumbled across some category-theoretic description of cell membranes... dagnabit. 67.198.37.16 (talk) 00:37, 16 May 2024 (UTC)