| Texto completo | |
| Autor(es): |
Correa, Eder M.
;
Galindo, Giovane
;
Grama, Lino
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | TRANSFORMATION GROUPS; v. N/A, p. 22-pg., 2025-10-27. |
| Resumo | |
In this paper, combining the Rashevsky-Chow-Sussmann (orbit) theorem with the Ambrose-Singer theorem, we introduce the notion of controllable principal connections on principal G-bundles. Using this concept, under a mild assumption of compactness, we estimate the Gromov-Hausdorff distance between principal G-bundles and certain reductive homogeneous G-spaces. In addition, we prove that every reduction of the structure group G to a closed connected subgroup gives rise to a sequence of Riemannian metrics on the total space for which the underlying sequence of metric spaces converges, in the Gromov-Housdorff topology, to a normal reductive homogeneous G-space. This last finding allows one to detect the presence of certain reductive homogeneous G-spaces in the Gromov-Housdorff closure of the moduli space of Riemannian metrics of the total space of the bundle through topological invariants provided by obstruction theory. (AU) | |
| Processo FAPESP: | 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos |
| Beneficiário: | Marco Antônio Teixeira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 22/10429-3 - Geometria hermitiana com torção em fibrados principais e aplicações |
| Beneficiário: | Eder de Moraes Correa |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 23/13131-8 - Estruturas Hermitianas Invariantes e Fluxos Geométricos em Espaços Homogêneos |
| Beneficiário: | Lino Anderson da Silva Grama |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |