dc.contributor | Marcio Gomes Soares | |
dc.contributor | Rogerio Santos Mol | |
dc.contributor | Fabio Enrique Brochero Martinez | |
dc.contributor | Thiago Fassarella Amaral | |
dc.contributor | Maurício Barros Corrêa Júnior | |
dc.creator | Luiz Guillermo Martinez Maza | |
dc.date.accessioned | 2019-08-10T08:04:02Z | |
dc.date.accessioned | 2022-10-03T22:52:07Z | |
dc.date.available | 2019-08-10T08:04:02Z | |
dc.date.available | 2022-10-03T22:52:07Z | |
dc.date.created | 2019-08-10T08:04:02Z | |
dc.date.issued | 2010-10-14 | |
dc.identifier | http://hdl.handle.net/1843/EABA-8CYHUK | |
dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/3812246 | |
dc.description.abstract | Let w be a holomorphic LDS r-form on a complex manifold M. In the case M = Cn, we show that if ker(w) admits a trivial subbundle of rank k, then there exists a holomrphic LDS (r - k)-form n on Cn such that ! is the exterior product of k with the product of k linearly independent global sections of ker(w). In the case that M is compact and connected we approach the classical Darboux-Jouanolou problem and we prove that if w has a suficiently large number of invariant analytic hypersurfaces, then w admits a meromorphic first integral. Next, we prove that if k >= r and w has k infinite families of w-invariant analytic hypersurfaces whose members intersect transversely, then w admits a meromorphic first integral of rank k. In particular, if k = r, thenw! is integrable. Continuing in this direction we prove that in the integrable case ! has a transversal structure by translations if and only if w is a multiples of a product of closed 1-forms. We conclude this work by showing that in the presence of a Kupka type singularity, there exists a coordinate system around the singularity such that w reduces to r+1 variables. In particular, w is integrable and the foliation induced by w has the product struture of a foliation by curves in Cr+1 multiplied by a regular foliation. | |
dc.publisher | Universidade Federal de Minas Gerais | |
dc.publisher | UFMG | |
dc.rights | Acesso Aberto | |
dc.subject | Codimensão | |
dc.subject | Folheações holomorfas | |
dc.title | Sobre distribuição e folheações holomorfas de codimensão maior do que um | |
dc.type | Tese de Doutorado | |