  Using the gauge/gravity correspondence, we study the properties of 2-point
correlation functions of finite-temperature strongly coupled gauge field
theories, defined on a curved space of general spatial topology with a dual
black hole description. We derive approximate asymptotic expressions for the
correlation functions and their poles, supported by exact numerical
calculations, and study their dependence on the dimension of spacetime and the
spatial topology. The asymptotic structure of the correlation functions depends
on the relation between the spatial curvature and the temperature, and is
noticeable when they are of the same order. In the case of a hyperbolic
topology, a specific temperature is identified for which exact analytical
solutions exist for all types of perturbations. The asymptotic structure of the
correlation functions poles is found to behave in a non-smooth manner when
approaching this temperature.
