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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 12, Pages 71–89
DOI: https://doi.org/10.26907/0021-3446-2023-12-71-89 (Mi ivm9927) 		 
Three-webs from circles

A.M. Shelekhov

Moscow Pedagogical State University, 1 Malaya Pirogovskaya str., bdg. 1, Moscow, 119991 Russia
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DOI: https://doi.org/10.26907/0021-3446-2023-12-71-89
Abstract: A new geometric necessary condition for regularity of a curved tree-web is found. A class of tree-webs from circles generalizing the regular tree-web of W. Blaschke from three elliptic bundles of circles with pairwise coinciding vertices is considered, and it is shown that only webs equivalent to the Blaschke web are regular in this class.
Keywords: curvilinear three-web, regular 3-web, three-webs from circles, three-web from pencils of circles, boundary curve of the 3-web, singular cycle of the three-web.
Received: 09.12.2022
Revised: 09.12.2022
Accepted: 29.03.2023
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2023, Volume 67, Issue 12, Pages 64–81
DOI: https://doi.org/10.3103/S1066369X23120083
Document Type: Article
UDC: 514.763
Language: Russian
Citation: A.M. Shelekhov, “Three-webs from circles”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 12, 71–89; Russian Math. (Iz. VUZ), 67:12 (2023), 64–81
Citation in format AMSBIB
\Bibitem{She23}
\by A.M.~Shelekhov
\paper Three-webs from circles
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 12
\pages 71--89
\mathnet{http://mi.mathnet.ru/ivm9927}
\crossref{https://doi.org/10.26907/0021-3446-2023-12-71-89}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2023
\vol 67
\issue 12
\pages 64--81
\crossref{https://doi.org/10.3103/S1066369X23120083}
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