  We discuss an infinite--dimensional k\"ahlerian manifold associated with the
area--preserving diffeomorphisms on two--dimensional torus, and,
correspondingly, with a continuous limit of the $A_r$--Toda system. In
particular, a continuous limit of the $A_r$--Grassmannians and a related
Pl\"ucker type formula are introduced as relevant notions for
$W_{\infty}$--geometry of the self--dual Einstein space with the rotational
Killing vector.
