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.

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Last modified: March 11, 2011