  Spin-orbit coupling plays a large role in stabilizing the low-temperature
orthorhombic phase of La$_{2-x}$Sr$_x$CuO$_4$. It splits the degeneracy of the
van Hove singularities (thereby stabilizing the distorted phase) and completely
changes the shape of the Fermi surfaces, potentially introducing diabolical
points into the band structure. The present paper gives a detailed account of
the resulting electronic structure.
  A slave boson calculation shows how these results are modified in the
presence of strong correlation effects. A scaling regime, found very close to
the metal-insulator transition, allows an analytical determination of the
crossover, in the limit of zero oxygen-oxygen hopping, $t_{OO}\rightarrow 0$.
Extreme care must exercised in chosing the parameters of the three-band model.
In particular, $t_{OO}$ is renormalized from its LDA value. Furthermore, it is
suggested that the slave boson model be spin-corrected, in which case the
system is close to a metal-insulator transition at half filling.
