Reduction of Volume—preserving Flows on an n—dimensional Manifold
Yong-aiZheng, De-binHuang, Zeng-rongLiu · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2003
A geometric reduction procedure for volume-preserving flows with a volume-preserving symme-try on an n-dimensional manifold is obtained.Instead of the coordinate-dependent theory and the concrete coordinate transformation,we xhow that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space.More generally,if it admits an r-parameter volume-preserving commutable symmetry,then the reduced folw preserves the corresponding (n-r)-dimensional volume form.