  We provide a consistent statistical-mechanical treatment for describing the
thermodynamics and the structure of fluids embedded in the hyperbolic plane. In
particular, we derive a generalization of the virial equation relating the bulk
thermodynamic pressure to the pair correlation function and we develop the
appropriate setting for extending the integral-equation approach of
liquid-state theory in order to describe the fluid structure. We apply the
formalism and study the influence of negative space curvature on two types of
systems that have been recently considered: Coulombic systems, such as the one-
and two-component plasma models, and fluids interacting through short-range
pair potentials, such as the hard-disk and the Lennard-Jones models.
