On new constructions in the Blaschke-Bol problem
Abstract
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.
- Authors:
-
- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
- Publication Date:
- OSTI Identifier:
- 22364222
- Resource Type:
- Journal Article
- Journal Name:
- Sbornik. Mathematics
- Additional Journal Information:
- Journal Volume: 205; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; CLASSIFICATION; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS
Citation Formats
Nilov, F K. On new constructions in the Blaschke-Bol problem. United States: N. p., 2014.
Web. doi:10.1070/SM2014V205N11ABEH004432.
Nilov, F K. On new constructions in the Blaschke-Bol problem. United States. https://doi.org/10.1070/SM2014V205N11ABEH004432
Nilov, F K. 2014.
"On new constructions in the Blaschke-Bol problem". United States. https://doi.org/10.1070/SM2014V205N11ABEH004432.
@article{osti_22364222,
title = {On new constructions in the Blaschke-Bol problem},
author = {Nilov, F K},
abstractNote = {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.},
doi = {10.1070/SM2014V205N11ABEH004432},
url = {https://www.osti.gov/biblio/22364222},
journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 11,
volume = 205,
place = {United States},
year = {Sun Nov 30 00:00:00 EST 2014},
month = {Sun Nov 30 00:00:00 EST 2014}
}
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