A~generalization of the Pogorelov--Stocker theorem on complete developable surfaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 1, pp. 247-252
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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.
@article{FPM_2006_12_1_a8,
author = {I. Kh. Sabitov},
title = {A~generalization of the {Pogorelov--Stocker} theorem on complete developable surfaces},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {247--252},
publisher = {mathdoc},
volume = {12},
number = {1},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_1_a8/}
}
TY - JOUR AU - I. Kh. Sabitov TI - A~generalization of the Pogorelov--Stocker theorem on complete developable surfaces JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2006 SP - 247 EP - 252 VL - 12 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2006_12_1_a8/ LA - ru ID - FPM_2006_12_1_a8 ER -
I. Kh. Sabitov. A~generalization of the Pogorelov--Stocker theorem on complete developable surfaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 1, pp. 247-252. http://geodesic.mathdoc.fr/item/FPM_2006_12_1_a8/