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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 1, Pages 187–224 (Mi izv2628)  

This article is cited in 2 scientific papers (total in 2 papers)

Isometric immersions of a cone and a cylinder

M. I. Shtogrin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We thoroughly analyse the method used by Pogorelov to construct piecewise-smooth tubular surfaces in $\mathbb R^3$ isometric to the surface of a right circular cylinder. The properties of the inverse images of edges of any tubular surface on its planar unfolding are investigated in detail. We find conditions on plane curves lying on the unfolding that enable them to be the inverse images of edges of some tubular surface. We make a refinement concerning the number of smooth pieces that form a piecewise-smooth tubular surface. We generalize Pogorelov's method from the surface of a right circular cylinder to that of a right circular cone.

Keywords: surface theory, surfaces in three-dimensional space.

DOI: https://doi.org/10.4213/im2628

Full text: PDF file (1259 kB)
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English version:
Izvestiya: Mathematics, 2009, 73:1, 181–213

Bibliographic databases:

Document Type: Article
UDC: 514.752.437
MSC: 53A05, 53C45, 74K25
Received: 26.02.2007

Citation: M. I. Shtogrin, “Isometric immersions of a cone and a cylinder”, Izv. RAN. Ser. Mat., 73:1 (2009), 187–224; Izv. Math., 73:1 (2009), 181–213

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Linking options:
  • http://mi.mathnet.ru/eng/izv2628
  • https://doi.org/10.4213/im2628
  • http://mi.mathnet.ru/eng/izv/v73/i1/p187

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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. M. I. Shtogrin, “Bending of a piecewise developable surface”, Proc. Steklov Inst. Math., 275 (2011), 133–154  mathnet  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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