<p>This paper is concerned with strongly pseudomonotone equilibrium problems on Hadamard manifolds. We first prove the existence and uniqueness of solution for this class of problems. We then establish lower and upper error bounds for strongly pseudomonotone equilibrium problems. Linear convergence and strong convergence of sequences generated by the modified projection method with suitable choices of step sizes are also investigated. Furthermore, we present finite convergence results, which are new even for the case of linear space setting, for the modified projection method under linear conditioning assumption. Some examples are given to support our results.</p>