Rigidity Theorem for Harmonic Maps from Riemannian Manifold to Grassmannian Manifold

We first study the Grassmannian manifold Gn, (R...) as a submanifold in Euclidean space A(R). Then we give a local expression for each map from Riemannian manifold M to Gn (R...) . A(R...) ), and use the local expression to establish a formula which is satisfied by any harmonic map from M to Gn (R...) ). As a consequence of this formula we get a rigidity theorem.