A generalization of the Pogorelov-Stocker theorem on complete developable surfaces (Q950819)

A theorem of [\textit{A. V. Pogorelov}, Extrinsic geometry of convex surfaces. Translations of Mathematical Monographs. Vol. 35. Providence, R.I.: American Mathematical Society (AMS). (1973; Zbl 0311.53067)] states, that any \(C^1-\)smooth, complete, developable surface of bounded exterior curvature in \(\mathbb R^3\) is cylindrical. \textit{J. J. Stoker} (see [Commun. Pure Appl. Math. 14, 627--635 (1961; Zbl 0114.36902)]) gave a generalization to \(C^2-\)smooth surfaces using a more general notion of completeness. The present paper extends Stoker's result to \(C^1-\)smooth surfaces which are normal developable in the Burago-Shefel' sense.