Abstract
We study local differential-geometrical properties of curvilinear k-webs defined by symmetric functions (webs SW(k)). This class of k-webs contains in particular algebraic rectilinear k-webs defined by algebraic curves of genus 0. On a web SW(3), there are three three-parameter families of closed Thomsen configurations. We find equations of a rectilinear web SW(k) in terms of adapted coordinates and prove that the curvature of a symmetric three-web is a skew-symmetric function with respect to adapted coordinates. In conclusion, we formulate some open problems.
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Original Russian Text © A.M. Shelekhov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 6, pp. 63–77.
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Shelekhov, A.M. Three-Webs Defined by Symmetric Functions. Russ Math. 62, 56–68 (2018). https://doi.org/10.3103/S1066369X18060063
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DOI: https://doi.org/10.3103/S1066369X18060063