Spheres in Hermitian Symmetric Spaces and Flag Manifolds

This paper contains a proof of the following property of compact irreducible Hermitian symmetric spaces. If H=G/K where G is a compact simply connected simple Lie group, T a maximal torus of G and F(T,H)=|E₁,...,E_m is the fixed point set of T on H, then for each pair E_i, E_j there is a 2-dimentional sphere N_ij H such that E_i and E_j are antipodal points of N_ij.