  This paper proposes a three-dimensional (3D) satellite-terrestrial
communication network assisted with reconfigurable intelligent surfaces (RISs).
Using stochastic geometry models, we present an original framework to derive
tractable yet accurate closed-form expressions for coverage probability and
ergodic capacity in the presence of fading. A homogeneous Poisson point process
models the satellites on a sphere, while RISs are randomly deployed in a 3D
cylindrical region. We consider nonidentical channels that correspond to
different RISs and follow the {\kappa}-{\mu} fading distribution. We verify the
high accuracy of the adopted approach through Monte Carlo simulations and
demonstrate the significant improvement in system performance due to using
RISs. Furthermore, we comprehensively study the effect of the different system
parameters on its performance using the derived analytical expressions, which
enable system engineers to predict and optimize the expected downlink coverage
and capacity performance analytically.
