  The pairing of charge carriers with large pair momentum is considered in
connection with high-temperature superconductivity of cuprate compounds. The
possibility of pairing arises due to some essential features of
quasi-two-dimensional electronic structure of cuprates: (i) The Fermi contour
with strong nesting features; (ii) The presence of extended saddle point near
the Fermi level; (iii) The existence of some ordered state (for example,
antiferromagnetic) close to the superconducting one as a reason for an
appearing of "pair" Fermi contour resulting from carrier redistribution in
momentum space. In an extended vicinity of the saddle point, momentum space has
hyperbolic (pseudoeuclidean) metrics, therefore, the principal values of
two-dimensional reciprocal reduced effective mass tensor have unlike signs.
Rearrangement of holes in momentum space results in a rise of "pair" Fermi
contour which may be defined as zero-energy line for relative motion of the
pair. The superconducting gap arises just on this line. Pair Fermi contour
formation inside the region of momentum space with hyperbolic metrics results
in not only superconducting pairing but in a rise of quasi-stationary state in
the relative motion of the pair. Such a state has rather small decay and may be
related to the pseudogap regime of underdoped cuprates. It is concluded that
the pairing in cuprates may be due to screened Coulomb repulsion. In this case,
the superconducting energy gap in hole-doped cuprates exists in the region of
hole concentration which is bounded both above and below. The superconducting
state with positive condensation energy exists in more narrow range of doping
level inside this region. Such hole concentration dependence correlates with
typical phase diagram of cuprates.
