  The observations of quantum oscillations in overdoped cuprate superconductors
were in agreement with a charge density contained in a cylindrical Fermi
surface but the frequencies of lightly doped compounds were much smaller than
expected. This was attributed to a topological transition into small pockets of
Fermi surface associated with the existence of the charge density wave
underlying superlattice. On the other hand, spectroscopic measurements
suggested that the large two-dimensional Fermi surface changes continuously
into a set of four disconnected arcs. Here we take into account the effect of
the pseudogap that limits the available $k$-space area where the Landau levels
are developed on the Luttinger theorem and obtain the correct carrier
densities. The calculations show how the disconnected arcs evolve into a closed
Fermi surface reconciling the experiments.
