With the aborative description of geometry and analytics,applying Cartan Method,gets the Euler equation of weakly harmonic maps from high dimension Riemann manifold to homogeneous space.

• 借助于几何上与分析上的精细刻画；利用卡坦方法；得到高维Riemann流形到齐次空间弱调和映射体现的具体Euler方程形式.