| dc.contributor | Universidade Estadual Paulista (UNESP) | |
| dc.creator | Agafonov, Serguei | |
| dc.date | 2015-04-27T11:55:57Z | |
| dc.date | 2016-10-25T20:46:49Z | |
| dc.date | 2015-04-27T11:55:57Z | |
| dc.date | 2016-10-25T20:46:49Z | |
| dc.date | 2014 | |
| dc.date.accessioned | 2017-04-06T08:09:15Z | |
| dc.date.available | 2017-04-06T08:09:15Z | |
| dc.identifier | Geometriae Dedicata, v. 176, n. 1, p. 87-115, 2014. | |
| dc.identifier | 1572-9168 | |
| dc.identifier | http://hdl.handle.net/11449/122674 | |
| dc.identifier | http://acervodigital.unesp.br/handle/11449/122674 | |
| dc.identifier | http://dx.doi.org/10.1007/s10711-014-9960-8 | |
| dc.identifier | 8731229576624291 | |
| dc.identifier | http://dx.doi.org/10.1007/s10711-014-9960-8 | |
| dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/933295 | |
| dc.description | Implicit ODE, cubic in derivative, generically has no infinitesimal symmetries even at regular points with distinct roots. Cartan showed that at regular points, ODEs with hexagonal 3-web of solutions have symmetry algebras of the maximal possible dimension 3. At singular points such a web can lose all its symmetries. In this paper we study hexagonal 3-webs having at least one infinitesimal symmetry at singular points. In particular, we establish sufficient conditions for the existence of non-trivial symmetries and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling in some coordinates. Using the obtained results, we provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection form is holomorphic at the singular point, 2) the web admits at least one infinitesimal symmetry at this point. As a by-product, a classification of hexagonal weighted homogeneous 3-webs is obtained. | |
| dc.language | eng | |
| dc.relation | Geometriae Dedicata | |
| dc.rights | info:eu-repo/semantics/closedAccess | |
| dc.subject | Hexagonal 3-web | |
| dc.subject | Infinitesimal symmetries | |
| dc.subject | Chern connection | |
| dc.subject | Implicit ODE | |
| dc.title | Local classification of singular hexagonal 3-webs with holomorphic Chern connection form and infinitesimal symmetries | |
| dc.type | Otro | |
