We first study the Grassmannian manifoldG n (Rn+p)as a submanifold in Euclidean space Λ n (R n+p). Then we give a local expression for each map from Riemannian manifoldM toG n (R n+p) ?Λ n (R n+p), and use the local...We first study the Grassmannian manifoldG n (Rn+p)as a submanifold in Euclidean space Λ n (R n+p). Then we give a local expression for each map from Riemannian manifoldM toG n (R n+p) ?Λ n (R n+p), and use the local expression to establish a formula which is satisfied by any harmonic map fromM toG n (R n+p). As a consequence of this formula we get a rigidity theorem.展开更多
文摘We first study the Grassmannian manifoldG n (Rn+p)as a submanifold in Euclidean space Λ n (R n+p). Then we give a local expression for each map from Riemannian manifoldM toG n (R n+p) ?Λ n (R n+p), and use the local expression to establish a formula which is satisfied by any harmonic map fromM toG n (R n+p). As a consequence of this formula we get a rigidity theorem.
