Geodesic
On hexagonal three-webs formed by Cartesian net and a family of circles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2018), pp. 79-93

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By the Elie Cartan's method we prove that there are only two types of regular three-webs formed by the Cartesian net and a family of circles: three-webs $(C_1)$, in which the family is formed by concentric circles, and the three-webs $(C_2)$, where all circles of the family have the same radius, and their centers lie on a line.
Keywords: curvilinear three–web, regular three-web, circle three–web, three-web curvature. 
@article{IVM_2018_10_a7,
     author = {A. M. Shelekhov},
     title = {On hexagonal three-webs formed by {Cartesian} net and a family of circles},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {79--93},
     publisher = {mathdoc},
     number = {10},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_10_a7/}
}
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A. M. Shelekhov. On hexagonal three-webs formed by Cartesian net and a family of circles. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2018), pp. 79-93. http://geodesic.mathdoc.fr/item/IVM_2018_10_a7/