  The energetics and transport properties of the polaron in the anisotropic
surface over liquid helium are investigated. The localization radii and the
energy of the ground and excited states are calculated using the variational
method within the hydrodynamic model of the polaron. In particular, we have
considered maximal anisotropy which corresponds to the system of electrons in
quasi-one-dimensional channels over liquid helium. The polaron binding energy
is found and the temperature for the polaron formation is estimated below 0.1
K. Solving the hydrodynamic equations for fluid velocities, the polaron
mobilities along and across the channel are determined. The possibility of
experimental observation of polarons by measuring the frequency of
spectroscopic transitions as well the mobility as functions of the holding
electric field is addressed.
