BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability
Hermitian geometry with torsion on principal bundles and applications
Next generation bundling: tackling multivariate data and visualization errors
| Full text | |
| Author(s): |
Correa, Eder M.
;
Galindo, Giovane
;
Grama, Lino
Total Authors: 3
|
| Document type: | Journal article |
| Source: | TRANSFORMATION GROUPS; v. N/A, p. 22-pg., 2025-10-27. |
| Abstract | |
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) | |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 22/10429-3 - Hermitian geometry with torsion on principal bundles and applications |
| Grantee: | Eder de Moraes Correa |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 23/13131-8 - Invariant Hermitian structures and geometric flows on homogeneous spaces |
| Grantee: | Lino Anderson da Silva Grama |
| Support Opportunities: | Regular Research Grants |