Geodesic
Three-webs defined by symmetrical functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 63-77.

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We consider local differential-geometrical properties of curvilinear $k$-webs defined by symmetric functions (the webs $SW(k)$). The algebraic rectilinear $k$-webs defined by algebraic curves of genus $0$ are the symmetric $k$-webs. We prove that $3$ three-parameter families of $T$-configurations are closed on every symmetric $k$-web. We find the equations of a rectilinear $SW(k)$-web in adapted coordinates. It is proved that the curvature of a $SW(k)$-web is a skew-symmetric function with respect to adapted coordinates. In conclusion, we formulate some unsolved problems.
Keywords: curvilinear $k$-web, symmetric $k$-web, $k$-web equations, rectilinear $k$-web, algebraic $k$-web, three-web curvature.
Mots-clés : Thomsen configuration 
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     author = {A. M. Shelekhov},
     title = {Three-webs defined by symmetrical functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {63--77},
     publisher = {mathdoc},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_6_a5/}
}
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A. M. Shelekhov. Three-webs defined by symmetrical functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 63-77. http://geodesic.mathdoc.fr/item/IVM_2018_6_a5/

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