The vector fields admitting one-parameter spatial symmetry group and their reduction

For a n_dimensional vector fields preserving some n_form, the following conclusion is reached by the method of Lie group. That is, if it admits an one_parameter, n_form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding (n-1)_form. In partic ular, while n=3, an important result can be directly got which is given by Mezie and Wiggins in 1994.