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Sbornik: Mathematics, 2014, Volume 205, Issue 11, Pages 1650–1667
DOI: https://doi.org/10.1070/SM2014v205n11ABEH004432 (Mi sm8320) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On new constructions in the Blaschke-Bol problem

F. K. Nilov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (637 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM2014v205n11ABEH004432
Abstract: We find several essentially new constructions of hexagonal $3$-webs based on a combination of quadratic and linear families of circles. They are used to construct $5$ new types of hexagonal $3$-webs, which is an advance in the solution of the Blaschke-Bol problem (1938) on the classification of such webs. Unlike many known examples, in our proofs we give an explicit parallelizing diffeomorphism. We give a brief survey of all known examples of hexagonal $3$-webs and their properties. In conclusion, we formulate several conjectures and open problems.
Bibliography: 13 titles.
Keywords: webs, webs of circles, hexagonal closure condition, pencil of circles, quadratic family of circles.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МК-5490.2014.1
Russian Foundation for Basic Research 13-01-12449
Received: 26.12.2013 and 28.08.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 11, Pages 125–144
DOI: https://doi.org/10.4213/sm8320
Bibliographic databases:
Document Type: Article
UDC: 514.763.7
MSC: 53A60
Language: English
Original paper language: Russian
Citation: F. K. Nilov, “On new constructions in the Blaschke-Bol problem”, Mat. Sb., 205:11 (2014), 125–144; Sb. Math., 205:11 (2014), 1650–1667
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2014v205n11ABEH004432
  • https://www.mathnet.ru/eng/sm/v205/i11/p125
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:246
    English version PDF:13
    References:58
    First page:57
     
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