  We consider the minimum Yang-Mills energy on the complete $G_{2}$-manifolds
and Calabi-Yau 3-folds,the connection $A$ is a stability Yang-Mills connection
on the $G$-bundle $E$.We prove that the connection must be a $G_{2}$-instanton
on $G_{2}$-manifold and the bundle is holomorphic on Calabi-Yau 3-fold with
holonomy $SU(3)$.
