On new constructions in the Blaschke-Bol problem
We find several essentially new constructions of hexagonal -webs based on a combination of quadratic and linear families of circles. They are used to construct new types of hexagonal -webs, which is an advance in the solution of the Blaschke-Bol problem (1938) on the classification of such webs. Unl...
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| Veröffentlicht in: | Sbornik. Mathematics 2014-01, Vol.205 (11), p.1650-1667 |
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| container_issue | 11 |
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| container_title | Sbornik. Mathematics |
| container_volume | 205 |
| creator | Nilov, F. K. |
| description | We find several essentially new constructions of hexagonal -webs based on a combination of quadratic and linear families of circles. They are used to construct new types of hexagonal -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 -webs and their properties. In conclusion, we formulate several conjectures and open problems. Bibliography: 13 titles. |
| doi_str_mv | 10.1070/SM2014v205n11ABEH004432 |
| format | Article |
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| ispartof | Sbornik. Mathematics, 2014-01, Vol.205 (11), p.1650-1667 |
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| language | eng |
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| source | IOP Publishing Journals; Alma/SFX Local Collection |
| subjects | CALCULATION METHODS CLASSIFICATION Construction hexagonal closure condition Mathematical analysis MATHEMATICAL METHODS AND COMPUTING MATHEMATICAL MODELS MATHEMATICAL SOLUTIONS pencil of circles Proving quadratic family of circles Webs webs of circles |
| title | On new constructions in the Blaschke-Bol problem |
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