By choosing distinguished cross-sections in the second variational formula for harmonic maps from manifolds with not too fast volume growth into certain submanifolds in the Euclidean space some Liouville typ0e theorems have been prooved in this article Two groups of symetries and their Lie algebra property of the modified KdV equation (Li Yi-Shen and Zhu Guo-Cheng, 1985) are extended to the general modified KdV equation and the Miura transformation between the general modified Kdv equatins is also established.