4-webs in the plane and their linearizability
| dc.creator | Goldberg, Vladislav V. | |
| dc.date | 2002-09-22 | |
| dc.date | 2003-04-14 | |
| dc.date.accessioned | 2026-07-07T06:33:18Z | |
| dc.date.available | 2026-07-07T06:33:18Z | |
| dc.description | We investigate the linearizability problem for different classes of 4-webs in the plane. In particular, we apply a recently found in [AGL] the linearizability conditions for 4-webs in the plane to confirm that a 4-web MW (Mayrhofer's web) with equal curvature forms of its 3-subwebs and a nonconstant basic invariant is always linearizable (this result was first obtained in [M 28]); it also follows from the papers [Na 96] and [Na98]). Using the same conditions, we also prove that such a 4-web with a constant basic invariant (Nakai's web) is linearizable if and only if it is parallelizable. We also study four classes of the so-called almost parallelizable 4-webs APW_a, a = 1, 2, 3, 4 (for them the curvature K = 0 and the basic invariant is constant on the leaves of the web foliation X_a), and prove that a 4-web APW_a is linearizable if and only if it coincides with a 4-web MW_a of the corresponding special class of 4-webs MW. The existence theorems are proved for all the classes of 4-webs considered in the paper. | |
| dc.description | LaTeX, 20 pages; revised version (corrected some typos and made some formulations more precise) | |
| dc.identifier | https://arxiv.org/abs/math/0209289 | |
| dc.identifier | http://arxiv.org/abs/math/0209289 | |
| dc.identifier | Acta Appl. Math., 80 (2004) no. 1, 35-55 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99146 | |
| dc.subject | Differential Geometry | |
| dc.title | 4-webs in the plane and their linearizability | |
| dc.type | text |