Calibrated geometries in Grassmann manifolds (Q1823486)

The method of calibrated geometries is employed to prove: Theorem. If k is an even integer \(\geq 4\), then in the real Grassmann manifold \(G_ kR^ n\), each subgrassmannian in the sequence \[ G_ kR^{k+1}\subset G_ kR^{k+2}\subset...\subset G_ kR^{n-1} \] is volume minimizing in its homology class. Moreover, any other minimizer in the same homology class is congruent to it.