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Tr. Mat. Inst. Steklova, 2008, Volume 263, Pages 227–250 (Mi tm794)  

This article is cited in 6 scientific papers (total in 6 papers)

Piecewise Smooth Developable Surfaces

M. I. Shtogrin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A. V. Pogorelov introduced developable surfaces with regularity (twice differentiability) violated along separate lines. In particular, the surface may not be smooth at all points of these lines (which form edges in this case). It is assumed that each point of the surface under consideration that belongs to a curvilinear edge (as well as any other interior point of this surface) has a neighborhood isometric to a Euclidean disk. In this paper we study the behavior of a developable surface near its curvilinear edge. It is proved that if two smooth pieces of a developable surface are adjacent along a curvilinear edge, then the spatial location of one of them in $\mathbb R^3$ is uniquely determined by that of the other.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 263, 214–235

Bibliographic databases:

UDC: 514.752.43
Received in June 2008

Citation: M. I. Shtogrin, “Piecewise Smooth Developable Surfaces”, Geometry, topology, and mathematical physics. I, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 263, MAIK Nauka/Interperiodica, Moscow, 2008, 227–250; Proc. Steklov Inst. Math., 263 (2008), 214–235

Citation in format AMSBIB
\by M.~I.~Shtogrin
\paper Piecewise Smooth Developable Surfaces
\inbook Geometry, topology, and mathematical physics.~I
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2008
\vol 263
\pages 227--250
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2008
\vol 263
\pages 214--235

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    This publication is cited in the following articles:
    1. M. I. Shtogrin, “Isometric immersions of a cone and a cylinder”, Izv. Math., 73:1 (2009), 181–213  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. M. I. Shtogrin, “Bending of a Developable Surface That Preserves Its Edge and Generators”, Proc. Steklov Inst. Math., 266 (2009), 251–259  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. I. Kh. Sabitov, “On the developable ruled surfaces of low smoothness”, Siberian Math. J., 50:5 (2009), 919–928  mathnet  crossref  mathscinet  isi
    4. Hornung P., “Fine level set structure of flat isometric immersions”, Arch. Ration. Mech. Anal., 199:3 (2011), 943–1014  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. I. Shtogrin, “Bending of a piecewise developable surface”, Proc. Steklov Inst. Math., 275 (2011), 133–154  mathnet  crossref  mathscinet  isi  elib  elib
    6. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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