Linearizability of d-webs, d \geq 4, on two-dimensional manifolds
| dc.creator | Akivis, Maks A. | |
| dc.creator | Goldberg, Vladislav V. | |
| dc.creator | Lychagin, Valentin V. | |
| dc.date | 2002-09-22 | |
| dc.date | 2004-03-31 | |
| dc.date.accessioned | 2026-07-07T06:33:18Z | |
| dc.date.available | 2026-07-07T06:33:18Z | |
| dc.description | We find d - 2 relative differential invariants for a d-web, d \geq 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f (x,y) and g_4 (x,y),...,g_d (x,y), then necessary and sufficient conditions for the linearizabilty of a d-web are two PDEs of the fourth order with respect to f and g_4, and d - 4 PDEs of the second order with respect to f and g_4,...,g_d. For d = 4, this result confirms Blaschke's conjecture on the nature of conditions for the linearizabilty of a 4-web. We also give Mathematica codes for testing 4- and d-webs (d > 4) for linearizability and examples of their usage. | |
| dc.description | LaTeX, 21 pages; revised version (modified the introduction, replaced Mathematica code for testing 5-webs for linearizability by that for testing d-webs (d > 4) and added the example of the Spence-Kummer 9-web) | |
| dc.identifier | https://arxiv.org/abs/math/0209290 | |
| dc.identifier | http://arxiv.org/abs/math/0209290 | |
| dc.identifier | Selecta Math., 10 (2004) no. 4 431-451 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99147 | |
| dc.subject | Differential Geometry | |
| dc.title | Linearizability of d-webs, d \geq 4, on two-dimensional manifolds | |
| dc.type | text |