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

High-$T_c$ superconductivity of electron systems with flat bands pinned to the Fermi surface