ABSTRACT

PRl9 A closed differential fonn W is invariant under the vector field X associated to a differential system iff the inner product of w and X is zero.

Proof The necessary condition is obvious because PRl8 and dw = 0 imply ixw = O. Conversely, if ixW = 0 and dw = 0 = ixdw, then PRI8 implies that w is invariant.