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Joseph O'Rourke
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Developable surfaces in $\mathbb{R}^4$

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

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

Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958