FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 1, PAGES 95-107

**Classification of regular circle three-webs up to circular
transformations**

V. B. Lazareva

Abstract

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A curvilinear three-web formed by three pencils of circles is
called a circle web.
Generally speaking, the circle three-web is not regular, i.e., it is
not locally diffeomorphic to a web formed by three families of
parallel straight lines.
In this paper, all regular circle three-webs are classified up to
circular transformations.
The main result is as follows: there exist $48$ nonequivalent (with
respect to circular transformations) types of regular three-webs.
Five of them contain $$¥^{3} nonequivalent webs each,
$11$ types
contain $$¥^{2} nonequivalent webs each,
$12$ types
contain $$¥^{1} nonequivalent webs each;
$5$ webs
admit a one-parameter group of automorphisms.

Location: http://mech.math.msu.su/~fpm/eng/k10/k101/k10108h.htm

Last modified: March 11, 2011