# Talk:Isometry (Riemannian geometry)

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Field:  Geometry

## examples

Could someone expand this with some examples? Is it correct (speaking of surfaces) that a doughnut is isometric to a teacup and is (only) locally-isometric to an egg? Or is it that a non-deformed doughnut is isometric only to another (scaled or rotated) non-deformed doughnut, and is locally-isometric to a plane but not to a saddle? Cesiumfrog (talk) 02:36, 26 June 2008 (UTC)

Uh, no no and no, I believe you are thinking of a homotopy, which is a completely different and unrelated thing. Isometries are things that preserve distances as things move about. Thus, rotating a coffee cup is an isometry, because the distance of lip to handle does NOT change. Anything else will change distances, and will not be an isometry. Point taken: this article needs a non-technical introduction. 67.198.37.16 (talk) 23:47, 24 September 2016 (UTC)

## Definition

Should it not read: "...diffeomorphism. Then ${\displaystyle g}$ is called an ..." --Oerms (talk) 16:35, 28 April 2009 (UTC)

Looks like it has been fixed. 67.198.37.16 (talk) 23:43, 24 September 2016 (UTC)