Symmetric structures on the cotangent bundles of the real and complex Grassmannians (Q1911883)

The present paper studies the homogeneous, the para-Kähler and the symmetric structures on the cotangent bundles of the complex and (oriented or unoriented) real Grassmannians. They are symmetric spaces in Berger's and Kaneyuki-Kozai's classifications [\textit{S. Kaneyuki} and \textit{M. Kozai}, Tokyo J. Math. 8, 483-490 (1985; Zbl 0592.53043)]. The cotangent bundle of the sphere and the real projective spaces are, moreover, harmonic symmetric spaces in \textit{A.-C. Allamigeon's} classification [C. R. Acad. Sci., Paris 243, 121-123 (1956; Zbl 0075.31701)].