Reduction of volume-preserving flows on an \(n\)-dimensional manifold (Q1873590)

Reduction of volume-preserving flows with volume-preserving symmetry on an \(n\)-dimensional manifold is obtained by using a geometric approach. It is shown that a volume-preserving flow which admits an \(r\)-parameter volume-preserving commutable symmetry on an \(n\)-dimensional manifold can be reduced to a volume-preserving flow on the corresponding \((n-r)\)-dimensional volume form. One example taken from the literature is re-done via this geometric approach. It would have been nice, though, to have seen an original example included.