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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
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
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
Linking options:
https://www.mathnet.ru/eng/im2628https://doi.org/10.1070/IM2009v073n01ABEH002443 https://www.mathnet.ru/eng/im/v73/i1/p187
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Abstract page: | 1981 | Russian version PDF: | 392 | English version PDF: | 14 | References: | 95 | First page: | 24 |
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