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Fundam. Prikl. Mat., 2006, Volume 12, Issue 1, Pages 247–252 (Mi fpm930)  

This article is cited in 3 scientific papers (total in 3 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.

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English version:
Journal of Mathematical Sciences (New York), 2008, 149:1, 1028–1031

Bibliographic databases:

UDC: 514.752

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

Citation in format AMSBIB
\Bibitem{Sab06}
\by I.~Kh.~Sabitov
\paper A~generalization of the Pogorelov--Stocker theorem on complete developable surfaces
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 1
\pages 247--252
\mathnet{http://mi.mathnet.ru/fpm930}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2249687}
\zmath{https://zbmath.org/?q=an:1156.53009}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 149
\issue 1
\pages 1028--1031
\crossref{https://doi.org/10.1007/s10958-008-0041-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38349191426}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. I. Shtogrin, “Piecewise Smooth Developable Surfaces”, Proc. Steklov Inst. Math., 263 (2008), 214–235  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Korobkov M.V., “Properties of $C^1$-smooth functions whose gradient range has topological dimension 1”, Dokl. Math., 81:1 (2010), 11–13  crossref  mathscinet  zmath  isi  elib  elib
    3. M. I. Shtogrin, “Bending of a piecewise developable surface”, Proc. Steklov Inst. Math., 275 (2011), 133–154  mathnet  crossref  mathscinet  isi  elib  elib
  • Фундаментальная и прикладная математика
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