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Fundamentalnaya i Prikladnaya Matematika, 2006, Volume 12, Issue 1, Pages 247–252
(Mi fpm930)
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This article is cited in 4 scientific papers (total in 4 papers)
A generalization of the Pogorelov–Stocker theorem on complete developable surfaces
I. Kh. Sabitov M. V. Lomonosov Moscow State University
Abstract:
The well-known Pogorelov theorem stating the cylindricity of any $C^1$-smooth, complete, developable surface of bounded exterior curvature in $\mathbb R^3$ 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 being normal developable in the Burago–Shefel' sense.
Citation:
I. Kh. Sabitov, “A generalization of the Pogorelov–Stocker theorem on complete developable surfaces”, Fundam. Prikl. Mat., 12:1 (2006), 247–252; J. Math. Sci., 149:1 (2008), 1028–1031
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https://www.mathnet.ru/eng/fpm930 https://www.mathnet.ru/eng/fpm/v12/i1/p247
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Abstract page: | 483 | Full-text PDF : | 182 | References: | 62 | First page: | 1 |
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