Algebraic, topological and analytical techniques in differential geometry and geom...
Orthogonal geodesics in manifolds with singular boundary. Applications to the theo...
Modern methods in differential geometry and geometric analysis
| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil
[2] Univ Murcia, Campus Espinardo, E-30100 Murcia - Spain
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Annali di Matematica Pura ed Applicata; v. 198, n. 1, p. 205-226, FEB 2019. |
| Web of Science Citations: | 3 |
| Abstract | |
In this paper we introduce the concept of singular Finsler foliation, which generalizes the concepts of Finsler actions, Finsler submersions and (regular) Finsler foliations. We show that if F is a singular Finsler foliation with closed leaves on a Randers manifold (M,Z) with Zermelo data (h,W), then F is a singular Riemannian foliation on the Riemannian manifold (M,h). As a direct consequence, we infer that the regular leaves are equifocal submanifolds (a generalization of isoparametric submanifolds) when the wind W is an infinitesimal homothety of h (e.g., when W is a Killing vector field or M has constant Finsler curvature). We also present a slice theorem that locally relates singular Finsler foliations on Finsler manifolds with singular Finsler foliations on Minkowski spaces. (AU) | |
| FAPESP's process: | 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 11/21362-2 - Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |