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

The well-known Pogorelov theorem stating the cylindricity of any C ¹-smooth, complete, developable surface of bounded exterior curvature in ℝ³ was generalized by Stocker to C ²-smooth surfaces with a more general notion of completeness. We extend Stocker’s result to C ¹-smooth surfaces that are normal developable in the Burago-Shefel’ sense. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 1, pp. 247–252, 2006.