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.
Russian Mathematics – Springer Journals
Published: May 30, 2018
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