On new constructions in the Blaschke-Bol problem
Journal Article
·
· Sbornik. Mathematics
- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
We find several essentially new constructions of hexagonal 3-webs based on a combination of quadratic and linear families of circles. They are used to construct 5 new types of hexagonal 3-webs, which is an advance in the solution of the Blaschke-Bol problem (1938) on the classification of such webs. Unlike many known examples, in our proofs we give an explicit parallelizing diffeomorphism. We give a brief survey of all known examples of hexagonal 3-webs and their properties. In conclusion, we formulate several conjectures and open problems. Bibliography: 13 titles.
- OSTI ID:
- 22364222
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 11 Vol. 205; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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