Template talk:Curvature

I'm not sure I agree that total curvature should be listed in this template. It doesn't fit in with all the others, since, for instance, all notions of curvature should be local, but total curvature is not. Instead, it is a functional of curvature, just like the Willmore energy for example. Jjauregui (talk) 15:55, 4 September 2008 (UTC)[reply]

I hadn't considered that, but I would support a more inclusive rather than less inclusive definition of curvature which would include not necessarily local things. Total curvature should be included since (1) it is called curvature, (2) it clearly involves the classical Frenet curvature, and (3) the integrand of the total curvature (in dimension greater than 2) is sometimes also called the total curvature (and is local). I'm not opposed to including non-local curvatures such as the Willmore energy (which has as a primitive the Willmore curvature) or curvatures which aren't really curvatures like the Q curvature and sigma invariant. siℓℓy rabbit (talk) 19:27, 4 September 2008 (UTC)[reply]