Isotropy representations of semisimple symmetric spaces and homogeneous hypersurfaces (Q1093934)

The isotropy representations of semisimple symmetric spaces produce orbits in the pseudo-Riemannian sphere. This paper deals with the case that the orbits are homogeneous hypersurfaces. Their geometry is studied, especially the principal curvatures and focal sets. A complete list of homogeneous hypersurfaces that are orbits under isotropy representations of semisimple symmetric spaces is given. In contrast to the positive definite case, not all homogeneous hypersurfaces in the pseudo-Riemannian sphere are orbits under an isotropy representation.