Singular riemannian foliations on simply connected spaces
| dc.creator | Alexandrino, Marcos M. | |
| dc.creator | Toeben, Dirk | |
| dc.date | 2004-11-18 | |
| dc.date.accessioned | 2026-07-07T06:30:39Z | |
| dc.date.available | 2026-07-07T06:30:39Z | |
| dc.description | A singular riemannian foliation on a complete riemannian manifold is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. The singular foliation is said to admit sections if each regular point is contained in a totally geodesic complete immersed submanifold that meets every leaf orthogonally and whose dimension is the codimension of the regular leaves. A typical example of such singular foliation is the partition by orbits of a polar action,e.g. the orbits of the adjoint action of a compact Lie group on itself. We prove that a singular riemannian foliation with compact leaves that admit sections on a simply connected space has no exceptional leaves, i.e., each regular leaf has trivial normal holonomy. We also prove that there exists a convex fundamental domain in each section of the foliation and in particular that the space of leaves is a convex Coxeter orbifold. | |
| dc.description | 17 pages, Latex 2e | |
| dc.identifier | https://arxiv.org/abs/math/0411415 | |
| dc.identifier | http://arxiv.org/abs/math/0411415 | |
| dc.identifier | Differential Geom. and Appl. 24 (2006) 383-397 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98392 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C12, 57R30 | |
| dc.title | Singular riemannian foliations on simply connected spaces | |
| dc.type | text |