Geodesic
A generalized theorem on curvilinear three-web boundaries and its applications
Sbornik. Mathematics, Tome 211 (2020) no. 3, pp. 422-454

Voir la notice de l'article provenant de la source Math-Net.Ru

Suppose that a curvilinear three-web is given by the equation $F(x,y,z)=0$. A specific structure of the derivatives of the function $F$ is established that characterizes regular three-webs. This makes it possible to list all regular three-webs formed by the Cartesian net and a family of circles, and also by the Cartesian net and a family of second-order curves. Bibliography: 4 titles.
Keywords: curvilinear three-web, regular three-web, circle three-web, three-web of conics. 
A. M. Shelekhov. A generalized theorem on curvilinear three-web boundaries and its applications. Sbornik. Mathematics, Tome 211 (2020) no. 3, pp. 422-454. http://geodesic.mathdoc.fr/item/SM_2020_211_3_a3/
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[1] A. M. Shelekhov, V. B. Lazareva, A. A. Utkin, Krivolineinye tri-tkani, Tverskoi gos. un-t, Tver, 2013, 237 pp. | Zbl

[2] W. Blaschke, Einführung in die Geometrie der Waben, Birkhäuser Verlag, Basel, Stuttgart, 1955, 108 pp. | MR | MR | Zbl

[3] V. B. Lazareva, A. M. Shelekhov, “On triangulations of the plane by pencils of conics”, Sb. Math., 198:11 (2007), 1637–1663 | DOI | DOI | MR | Zbl

[4] M. A. Polovtseva, “O nekotorykh determinantnykh mnogoobraziyakh v $\mathbb{P}^5$ i $\mathbb{P}^9$ kak obrazakh algebraicheskikh sistem ploskikh krivykh vtoroi i tretei stepeni”, Konstruktivnaya algebraicheskaya geometriya, Resp. sb. nauch. tr., 190, Yaroslavskii ped. in-t, Yaroslavl, 1980, 100–114