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

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!

Is there are classification of the equivalent of a developable surface in $\mathbb{R}^4$? Analogous to: planes, cylinders, cones, and tangent developables in $\mathbb{R}^3$? Here I am imagining "developing" a 3-dimensional manifold embedded in $\mathbb{R}^4$ into $\mathbb{R}^3$.

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!

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