Symmetric structures on the cotangent bundles of the real and complex Grassmannians

The geometric structure of the cotangent bundles of the real oriented, real unoriented and complex Grassmann manifolds is studied. They are symmetric spaces in Berger's and Kaneyuki-Kozai's classifications. The cotangent bundle of the sphere and the real projective space are moreover harmonic symmetric spaces in Allamigeon's classification.