curvature of a bended piece of paper?

Question

According to the Theorema Egregium, a surface that is transformed isometrically, retains its gaussian curvature at every point.

This means that for example a piece of paper cannot be folded into a sphere. We could do it with pizza dough, but paper cannot stretch.

However, If we bend a piece of paper, it is still in some way "curved" (in the intuitive sense).

Similarly, if I'm correct, a cilinder has the same covariant derivative as a flat plane at each point, even though it is in some intuitive sense "curved".

What would we call this "curvedness" of a cilinder and a bended piece of paper, which don't have gaussian curvature?

Answer 1

Hint:

Th Gaussian curvature of a surface is the product of two principal curvatures, so it is null if one of the two curvatures is null. This is the case of a cylinder and of a bended paper.

The not null curvature, in these cases, can be called a normal curvature.