Talk:Geodesic curvature

Isn't the first of the theorems mentioned just a definition, namely the definition given in the text above it?

Geodesic Curvature Unsigned?

Is scalar geodesic curvature the magnitdue of the vector, or the determinant of the projection onto the tangent plane and the tangent vector? I am looking the other things that refer to geodesic curvature and I can not figure out how the citing articles can use it unless it is signed. 149.169.152.14 20:04, 12 January 2007 (UTC)[reply]

why submanifold?

Geodesic curvature is defined for a curve in any riemannian manifold. It is artificial to assume that the manifold is a submanifold in another manifold. The page should be corrected. Tkuvho (talk) 13:28, 14 February 2012 (UTC)[reply]

Actually, geodesic curvature can be defined without the presence of a submanifold, but it is then plain curvature (though one can call it geodesic curvature as well). The whole point of defining geodesic curvature is when a curve is contained in a submanifold. I have changed the page to reflect this, and hope it is clearer that way.

Just like curves in space, there is no notion of sign, because this requires orienting two vectors, which is only possible in dimension 2. Pascalromon (talk) 21:34, 7 January 2014 (UTC)[reply]

Meaningless statement

The section Some results involving geodesic curvature contains this sentence:

"The geodesic curvature is none other than the usual curvature of the curve when computed intrinsically in the submanifold M."

But who knows what "the usual curvature" means? No one does. This is typical of the most unhelpful types of writing that appear in Wikipedia. If "the usual curvature" means anything, why not say what it means?Daqu (talk) 20:23, 9 August 2015 (UTC)[reply]

I think it is kind of clear to me NoetherianDomain (talk) 01:23, 26 April 2022 (UTC)[reply]