7.With the aborative description of geometry and analytics,applying Cartan Method,gets the Euler equation of weakly harmonic maps from high dimension Riemannmanifold to homogeneous space.
8.Let M be a compact n-dimensional Riemannmanifold, RicM≥n-1, Let d denote the diameter of M. In this paper. We prove the first eigenvalue of Laplacian operator λ 1≥π 2d 2+n-12.