Is there are classification of the equivalent of a "developable surface" in $\mathbb{R}^4$? Analogous to: planes, cylinders, cones, and tangent developables in $\mathbb{R}^3$? <b>Edit:</b> 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 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!