Moser's trick
= Moser's trick
{c}
{wiki}
Let $M$ be compact and let $\omega_t$ be a smooth family of symplectic forms with constant <de Rham cohomology> class. Choose $\sigma_t$ smoothly so that $\dot\omega_t=d\sigma_t$, solve
$$
\iota_{X_t}\omega_t=-\sigma_t,
$$
and let $\phi_t$ be the flow of $X_t$. Then
$$
\frac d{dt}(\phi_t^*\omega_t)
=\phi_t^*(\dot\omega_t+\mathcal L_{X_t}\omega_t)=0,
$$
so $\phi_t^*\omega_t=\omega_0$.
= Moser theorem
{c}
{synonym}