On the Geometry of the Orbits of Hermann Actions
Differential Geometry
2007-12-10 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0701731,
title = {On the Geometry of the Orbits of Hermann Actions},
author = {Oliver Goertsches and Gudlaugur Thorbergsson},
journal= {arXiv preprint arXiv:math/0701731},
year = {2007}
}
Comments
22 pages