= Presymplectic form
{title2=$d\omega=0,\quad\operatorname{rank}\omega=\mathrm{constant}$}
A <presymplectic form> is a closed <two-form>, commonly assumed to have constant rank, that need not be nondegenerate. A <symplectic form> is its nondegenerate special case. Its kernel distribution is integrable: for kernel fields $X,Y$, the identity $d\omega=0$ gives $\iota_{[X,Y]}\omega=0$. If the characteristic leaf quotient is smooth and the form descends, that quotient has a <symplectic form>. A regular <Hamiltonian> energy hypersurface carries such a form with kernel spanned by its <Hamiltonian vector field>.
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