Feuilletages riemanniens singuliers transversalement intégrables
Let be a compact Lie group acting in a Hamiltonian way on a symplectic manifold which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map is proper so that the reduced space is compact for all . Then, we can define the “formal geometric quantization” of asThe aim of this article is to study the functorial properties of the assignment .
The exceptional compact symmetric spaces and admit cohomogeneity one isometric actions with two totally geodesic singular orbits. These singular orbits are not reflective submanifolds of the ambient spaces. We prove that the radial unit vector fields associated to these isometric actions are harmonic and minimal.