  For several classes of second order dispersionless PDEs, we show that the
symbols of their formal linearizations define conformal structures which must
be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is
integrable by the method of hydrodynamic reductions. This demonstrates that the
integrability of these dispersionless PDEs can be seen from the geometry of
their formal linearizations.
