Geodesic
Three-webs from circles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2023), pp. 71-89

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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. 
@article{IVM_2023_12_a5,
     author = {A.M. Shelekhov},
     title = {Three-webs from circles},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {71--89},
     publisher = {mathdoc},
     number = {12},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_12_a5/}
}
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A.M. Shelekhov. Three-webs from circles. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2023), pp. 71-89. http://geodesic.mathdoc.fr/item/IVM_2023_12_a5/