Singular riemannian foliations on simply connected spaces

Details Singular riemannian foliations on simply connected spaces Singular riemannian foliations on simply connected spaces

2004-11-18

arxiv.org/abs/math/0411415v1

Differential Geom. and Appl. 24 (2006) 383-397

Mathematics

Differential Geometry

17 pages, Latex 2e

Scientific paper

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.

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