Contact conformal factor along an isotopy
= Contact conformal factor along an isotopy
{title2=$u_t(x)=\exp\!\left(\int_0^t h_s(\rho_s(x))\,ds\right)$}
If a <time-dependent vector field> satisfies $\dot\alpha_t+\mathcal L_{Y_t}\alpha_t=h_t\alpha_t$, its <flow maps> satisfy $\rho_t^*\alpha_t=u_t\alpha_0$, where $u_t(x)=\exp(\int_0^t h_s(\rho_s(x))\,ds)$. Thus the conformal factor is smooth and positive even when $h_t$ changes sign.