具有单参数空间对称群的向量场及其约化

The Vector Fields Admitting One-Parameter Spatial Symmetry Group and Their Reduction

对于保持某n_形式的n维向量场,应用Lie群的方法得到结论:当这类向量场有保持n_形式的空间单参数对称群时,可具体地构造出一个与该向量场无关的变换,它不仅使向量场约化掉一维,并且使得约化向量场保持相应的(n-1)_形式· 特别,当n=3时,简单地得到了Mezie和Wiggins最近得到的重要结果·

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 a 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 particular, while n=3, an important result can be directly got which is given by Mezie and Wiggins in 1994.