This is discussed thoroughly in section 42 of "Differential Geometry of Two Dimensional Surfaces in Hyperspace" by E.B. Wilson and C.L.E Moore. The entire book "Proceedings of the American Academy of Arts and Sciences" (volume 52) is available from Google Books or from the archive.

This is discussed thoroughly in section 42 of "Differential Geometry of Two Dimensional Surfaces in Hyperspace" by E.B. Wilson and C.L.E Moore. The entire book "Proceedings of the American Academy of Arts and Sciences" (volume 52) is available from Google Books or from the archive.

I think it makes sense to define a developable hypersurface as the envelope of a one parameter family of hyperplanes, this way it seems clear that in codimension 1 there is a foliation by hyperplanes. (See exercise 4.63 in the notes "Intorduction to Differential Geometry" by Robbin and Salamon)