35 research outputs found
On the Geometry of the Orbits of Hermann Actions
We investigate the submanifold geometry of the orbits of Hermann actions on
Riemannian symmetric spaces. After proving that the curvature and shape
operators of these orbits commute, we calculate the eigenvalues of the shape
operators in terms of the restricted roots. As applications, we get a formula
for the volumes of the orbits and a new proof of a Weyl-type integration
formula for Hermann actions.Comment: 22 page