This article is cited in 2 papers

A generalized theorem on curvilinear three-web boundaries and its applications

A. M. Shelekhov

Moscow Pedagogical State University, Moscow, Russia

Abstract: 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.

UDC: 514.763.7

MSC: Primary 53A60; Secondary 14C21

Received: 10.09.2018 and 03.03.2019

DOI: 10.4213/sm9167

 English version: Sbornik: Mathematics, 2020, 211:3, 422–454

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