Classification of regular three-webs formed by pencils of circles (Q941975)

Using the Darboux projective interpretation of a variety of circles on the plane and a theorem on boundary curves of a three-web, the author proves that there exist no regular circular three-webs, except for those eight classes of them listed by \textit{V. B. Lazareva} [Webs and quasigroups, Kalinin 1988, 74--77 (1988; Zbl 0659.53022)]. Thus, the problem of finding all classes of regular webs formed by three pencils of circles, which was posed by \textit{W. Blaschke} in 1953 [see Einführung in die Geometric der Waben. Basel etc.: Birkhäuser (1955; Zbl 0068.36501)], is completely answered.