Abelian Equations and Rank Problems for Planar Webs
| dc.creator | Goldberg, Vladislav V. | |
| dc.creator | Lychagin, Valentin V. | |
| dc.date | 2006-05-04 | |
| dc.date.accessioned | 2026-07-07T07:13:55Z | |
| dc.date.available | 2026-07-07T07:13:55Z | |
| dc.description | We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincaré's theorem: a planar 4-web of maximum rank is linearizable. We also find an invariant intrinsic characterization of planar 4-webs of rank two and one and prove that in general such webs are not linearizable. This solves the Blaschke problem ``to find invariant conditions for a planar 4-web to be of rank 1 or 2 or 3''. Finally, we find invariant characterization of planar 5-webs of maximum rank and prove than in general such webs are not linearizable. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605124 | |
| dc.identifier | http://arxiv.org/abs/math/0605124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112661 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A60 | |
| dc.title | Abelian Equations and Rank Problems for Planar Webs | |
| dc.type | text |