Must a developable surface be ruled? The definition of developable surface requires it , of course, to be ruled. But what if I just assume literally the definition of developable surface is just locally in an open neighborhood $U$ isometric to an Euclidean space? Because this definition comes naturally from the "word", it is developed from a plane space. And I have seen some cases, where the surface's Gaussian curvature is identically zero but is not ruled, which is constructed by $\exp(-x^{-2})$. Is that surface developable in my sense.
Developable surface and ruled surface.
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differential-geometry
surfaces