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Izvestiya: Mathematics, 2009, Volume 73, Issue 1, Pages 181–213
DOI: https://doi.org/10.1070/IM2009v073n01ABEH002443 (Mi im2628) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Isometric immersions of a cone and a cylinder

M. I. Shtogrin

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (971 kB) Citations (6)
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DOI: https://doi.org/10.1070/IM2009v073n01ABEH002443
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.
Received: 26.02.2007
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2009, Volume 73, Issue 1, Pages 187–224
DOI: https://doi.org/10.4213/im2628
Bibliographic databases:
Document Type: Article
UDC: 514.752.437
MSC: 53A05, 53C45, 74K25
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v73/i1/p187
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    This publication is cited in the following 6 articles:
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:95
    First page:24
     
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