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Sbornik: Mathematics, 2001, Volume 192, Issue 1, Pages 65–87
DOI: https://doi.org/10.1070/sm2001v192n01ABEH000536
(Mi sm536)
 

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
References:
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
Russian version:
Matematicheskii Sbornik, 2001, Volume 192, Number 1, Pages 67–88
DOI: https://doi.org/10.4213/sm536
Bibliographic databases:
UDC: 513.7
MSC: 53C45, 53C42
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/sm536
  • https://doi.org/10.1070/sm2001v192n01ABEH000536
  • https://www.mathnet.ru/eng/sm/v192/i1/p67
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:436
    Russian version PDF:195
    English version PDF:20
    References:57
    First page:1
     
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