ABSTRACT
If a closed one-form a is in involution with closed one-forms p and r. prove ex is in involution with the Poisson bracket {P, y }.
Answer. We must prove:
(j)(a# , { p,y }#) = 0 . We have (by playing):
(j)(a#, {P,y}#)= (j)(a# ,[P# ,y#])
but
= a([p# ,y#])
since [Lx,ir ] = h,lJ
ip.a = ll>(a#,p#)
and thus the involution assumptions:
lead to the proof.
