<p>We provide five techniques for solving variational inequality problems on Hadamard manifolds that are based on the adaptive extragradient method. These algorithms operate adaptively, eliminating the need for prior knowledge of the Lipschitz constant associated with the vector field. Furthermore, the iterative sequences produced by the algorithms are shown to converge to the solution of the problem under the conditions that the vector fields are pseudo-monotone and Lipschitz continuous. Additionally, we establish global error bounds and <i>R</i>-linear convergence rates when the vector fields exhibit strong pseudo-monotonicity. Lastly, the theoretical results are illustrated with two numerical instances.</p>