In this paper,suppose M is a complete Riemannian manifold,and satifies dim HD( M) =1 ; then any harmonic m ap from M to a C-H manifold m ust be constant map was proved.

• 本文证明了完备非紧 Riemann流形 M；若其上不存在非常数、具有限 Dirichlet积分的调和函数 ；则从 M出发到任何 C-H流形的具有限能量的调和映照必为常值映照 .