While actual deformation in 3D space is not AE’s thing, I won’t say it can’t be done… I’ve seen things done with AE’s 3D space that makes me wonder why anyone would do it in AE, but looks incredible!
You might want to start your search by looking for a “fluttering leaf”, or something along those lines… I remember a tutorial for that, and applied to “paper” it would be pretty good.
https://forums.creativecow.net/thread/2/912397
is at least one discussion on that… there’s a lot of material out there.
As far as the “curling/bending” part, even though they are really 2D, there’s the new supercool puppet tool (see Aharon’s video tutorial), and a number of tried and true things like displacement maps, the cc sphere or cylinder, bezier warp. Although these don’t really bend 3D space, they look like it.
After all that, a 3D app is preferred because it allows “forces” like wind and gravity to act on an object, and the internal motion of the paper is easier as well, as a 3D app will support a mesh that makes deformation easier.