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This article is cited in 1 scientific paper (total in 1 paper)
Type number and rigidity of fibred surfaces
P. E. Markov Rostov State University
Abstract:
Infinitesimal $l$-th order bendings, $1\leqslant l\leqslant\infty$, of higher-dimensional surfaces are considered in higher-dimensional flat spaces (for $l=\infty$ an infinitesimal bending is assumed to be an analytic bending). In terms of the Allendoerfer type number, criteria are established for the $(r,l)$-rigidity (in the terminology of Sabitov) of such surfaces. In particular, an $(r,l)$-infinitesimal analogue is proved of the classical theorem of Allendoerfer on the unbendability of surfaces with type number $\geqslant 3$ and the class of $(r,l)$-rigid fibred surfaces is distinguished.
Received: 11.11.1999
Citation:
P. E. Markov, “Type number and rigidity of fibred surfaces”, Mat. Sb., 192:1 (2001), 67–88; Sb. Math., 192:1 (2001), 65–87
Linking options:
https://www.mathnet.ru/eng/sm536https://doi.org/10.1070/sm2001v192n01ABEH000536 https://www.mathnet.ru/eng/sm/v192/i1/p67
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Abstract page: | 436 | Russian version PDF: | 195 | English version PDF: | 20 | References: | 57 | First page: | 1 |
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