Maximal projective subspaces in the variety of planar normal sections of a flag manifold (Q1301602)

The authors study those subvarieties of the variety \(X[M]\) of planar normal sections on a natural embedding of a flag manifold \(M\), that are projective spaces. When \(M=G/T\) is the manifold of complete flags of a compact simple Lie group \(G\), those subspaces of the tangent space \(T[T](M)\), invariant by the torus action, give rise to real projective spaces of \(X[M]\).