  The phenomenon of flat bands pinned to the Fermi surface is analyzed on the
basis of the Landau-Pitaevskii relation, which is applicable to electron
systems of solids. It is shown that the gross properties of normal states of
high-$T_c$ superconductors, frequently called strange metals, are adequately
explained within the flat-band scenario. Most notably, we demonstrate that in
electron systems moving in a two-dimensional Brillouin zone, superconductivity
may exist in domains of the Lifshitz phase diagram lying far from lines of
critical antiferromagnetic fluctuations, even if the effective
electron-electron interaction in the Cooper channel is repulsive.
