FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 1, PAGES 247-252

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

I. Kh. Sabitov

Abstract

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The well-known Pogorelov theorem stating the cylindricity of any $C1$-smooth, complete, developable surface of bounded exterior curvature in $$R³ was generalized by Stocker to $C2$-smooth surfaces with a more general notion of completeness. We extend Stocker's result to $C1$-smooth surfaces being normal developable in the Burago--Shefel' sense.

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Last modified: July 8, 2006