Invariant fourth root Finsler metrics on the Grassmannian manifolds (Q617933)

The authors investigate invariant fourth root Finsler metrics on the real Grassmannian manifolds \(SO(p+q)/SO(p)\times SO(q)\). In the first case \(p=q=2\), using the results from the theory of invariant polynomials of Lie groups, the classification by means of the decomposition of the isotropic representation and the invariant Riemannian metrics are obtained. In the second case \(p>2, q\geq 2\) the isotropy representation is irreductible and the classification through developing an invariant theory is given.