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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 6, Pages 63–77 (Mi ivm9368)  

Three-webs defined by symmetrical functions

A. M. Shelekhov

Tver State University, 33 Zhelyabov str., Tver, 170000 Russia

Abstract: 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, Thomsen configuration, rectilinear $k$-web, algebraic $k$-web, three-web curvature.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:6, 56–68

Bibliographic databases:

Document Type: Article
UDC: 514.763
Received: 06.04.2017

Citation: A. M. Shelekhov, “Three-webs defined by symmetrical functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 6, 63–77; Russian Math. (Iz. VUZ), 62:6 (2018), 56–68

Citation in format AMSBIB
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\by A.~M.~Shelekhov
\paper Three-webs defined by symmetrical functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 6
\pages 63--77
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\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 6
\pages 56--68
\crossref{https://doi.org/10.3103/S1066369X18060063}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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