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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 246, Pages 66–83 (Mi znsl549)  

This article is cited in 4 scientific papers (total in 4 papers)

Some bendings of the long cylinder

V. A. Zalgaller

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (300 kB) Citations (4)
Abstract: The peace-linear isometric embeddings of the cylindrical surfaces in $\mathbb R^3$ are described by elementary means. Let $T^2$ be a flat torus, and $\gamma$ the shortest closed geodesics on this torus of length $l_0$. Let $l$ be the length of some closed geodesics on $T^2$, which is not homotopic to $\gamma$, nor to any power of $\gamma$ and $l>kl_0$. It is demonstrated how for sufficiently large $k$ the torus $T^2$ can be embedded into $\mathbb R^3$. The same is done for the skew flat torus. For any type of knot in $\mathbb R^3$ and for sufficiently large $k$, in the isometrical embedding of the torus $T^2$ into $\mathbb R^3$ is described as a tube knotted as the above-mentioned knot.
Received: 24.07.1996
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 100, Issue 3, Pages 2228–2238
DOI: https://doi.org/10.1007/s10958-000-0007-3
Bibliographic databases:
UDC: 514.113, 514.752.43
Language: Russian
Citation: V. A. Zalgaller, “Some bendings of the long cylinder”, Geometry and topology. Part 2, Zap. Nauchn. Sem. POMI, 246, POMI, St. Petersburg, 1997, 66–83; J. Math. Sci. (New York), 100:3 (2000), 2228–2238
Citation in format AMSBIB
\Bibitem{Zal97}
\by V.~A.~Zalgaller
\paper Some bendings of the long cylinder
\inbook Geometry and topology. Part~2
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 246
\pages 66--83
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl549}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1631780}
\zmath{https://zbmath.org/?q=an:0936.53004}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 100
\issue 3
\pages 2228--2238
\crossref{https://doi.org/10.1007/s10958-000-0007-3}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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