Orthogonally transversal submanifolds and the generalizations of the Weyl group (Q1069142)

This paper discusses a generalization of the concept of a Weyl group for certain isometric actions of a compact Lie group on a Riemannian manifold and its relation to earlier such generalizations. The approach requires the existence of an orthogonally transversal submanifold S which means that S meets each orbit of the action and is orthogonal to the orbits at each point. Necessary as well as various sufficient conditions for the existence of S are given. The points of S with singular orbits are contained in a finite union of codimension 1, totally geodesic submanifolds of S. These are called the walls. The generalized Weyl group is the group generated by certain generalized reflections in the walls.