Definition talk:Curvature of Curve Parameterized by Arc Length/3-Dimensional Real Vector Space

It's a highly specalised definition this one.

Is there a more general form of which it is merely possible to say that this is just a specific instance? --prime mover (talk) 16:59, 22 November 2022 (UTC)

Do you mean for curves in $\R^n$ for $n \ge 4$? One can define it but probably not so interesting.

On manifolds, you cannot define a similar thing because $\alpha ' '$ does not exist.

On the other hand, for $\R^2$ we already have Definition:Curvature. That is more informative definition. In $\R^2$ you can say curvature is positive if it curves to the right, and negative if it curves to the left. But in $\R^3$ there is no such thing. --Usagiop (talk) 17:34, 22 November 2022 (UTC)

Yes, the elementary curve theory is special. --Usagiop (talk) 17:39, 22 November 2022 (UTC)