Classification of regular circle three-webs up to circular transformations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 95-107
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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 $\infty^3$ nonequivalent webs each, 11 types contain $\infty^2$ nonequivalent webs each, 12 types contain $\infty^1$ nonequivalent webs each; 5 webs admit a one-parameter group of automorphisms.
@article{FPM_2010_16_1_a7,
author = {V. B. Lazareva},
title = {Classification of regular circle three-webs up to circular transformations},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {95--107},
publisher = {mathdoc},
volume = {16},
number = {1},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a7/}
}
V. B. Lazareva. Classification of regular circle three-webs up to circular transformations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 95-107. http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a7/