Abstract:
We construct a closed orientable polyhedral surface of arbitrary genus that is embedded in three-dimensional Euclidean space and admits a one-parameter bending under which all its handles bend. This surface admits no other bendings. We also construct a flexible closed nonorientable polyhedral surface of arbitrary genus such that all its handles and Möbius strips bend during its bending.
Citation:
M. I. Shtogrin, “On flexible polyhedral surfaces”, Geometry, topology, and applications, Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 288, MAIK Nauka/Interperiodica, Moscow, 2015, 171–183; Proc. Steklov Inst. Math., 288 (2015), 153–164
\Bibitem{Sht15}
\by M.~I.~Shtogrin
\paper On flexible polyhedral surfaces
\inbook Geometry, topology, and applications
\bookinfo Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 288
\pages 171--183
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3592}
\crossref{https://doi.org/10.1134/S0371968515010124}
\elib{https://elibrary.ru/item.asp?id=23302189}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 288
\pages 153--164
\crossref{https://doi.org/10.1134/S0081543815010125}
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Linking options:
https://www.mathnet.ru/eng/tm3592
https://doi.org/10.1134/S0371968515010124
https://www.mathnet.ru/eng/tm/v288/p171
This publication is cited in the following 5 articles:
V. A. Alexandrov, E. P. Volokitin, “An embedded flexible polyhedron with nonconstant dihedral angles”, Siberian Math. J., 65:6 (2024), 1259–1280
V. Alexandrov, “The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in R-D does not always remain unaltered during the flex”, J. Geom., 111:2 (2020), 32
D. I. Sabitov, I. Kh. Sabitov, “Mnogochleny ob'ema dlya mnogogrannikov kombinatornogo tipa n-grannykh prizm v sluchayakh n=5,6,7”, Sib. elektron. matem. izv., 16 (2019), 439–448
V. Alexandrov, “A sufficient condition for a polyhedron to be rigid”, J. Geom., 110:2 (2019), UNSP 38
I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175
Citation in format AMSBIB
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