Talk:Riemannian manifold: Difference between revisions

 

A Riemannian manifold means that the metric is smooth. This is the default mathematical convention and other pages on Wikipedia invariably agree with this. It is very unusual for the word "Riemannian manifold" to mean that there is no regularity at all on the metric, as was previously the case on this page. In geometric analysis, one considers things that are "almost Riemannian manifolds", but the case when you just so happen to have an honest-to-goodness smooth manifold with an honest-to-goodness non-regular metric is a very special case that shouldn't be the default assumption on this page. More often, the "almost Riemannian manifolds" considered in geometric analysis aren't even smooth manifolds! Indeed, if you look at the main source for the content on the previous versions of this page about the non-smooth case (Gromov), you will see that the results this page cites from it are actually not about smooth manifolds with non-regular metrics, but about much weaker spaces. [[User:Mathwriter2718|Mathwriter2718]] ([[User talk:Mathwriter2718|talk]]) 19:22, 25 June 2024 (UTC)