Is there a classification of the equivalent of a "developable surface" in $\mathbb{R}^4$?
Analogous to: planes, cylinders, cones, and tangent developables in $\mathbb{R}^3$?
**Edit:** Here I am imagining "developing" a 3-dimensional manifold embedded in $\mathbb{R}^4$ into
$\mathbb{R}^3$. (Apologies for the earlier misleading version!)

I would appreciate any suggestions for source materials here. My only source
(**Edit:** now evidently misleading)
is one page (p.342) in Hilbert and Cohn-Vossen (*Geometry and the Imagination*), in which they say: in $\mathbb{R}^4$

there are surfaces that are isometric to the Euclidean plane in the small but are not ruled.

But now I see from the comments that this must mean a two-dimensional surface embedded in $\mathbb{R}^4$, which is not exactly what I seek.

A precise definition of *developable 3-manifold* in $\mathbb{R}^d$ would also be much appreciated.
Thanks for pointers!