Developing artificial agents that unify representation, memory, adaptation, and prediction remains a fundamental challenge in artificial intelligence. Here we introduce a geometric framework in which cognitive computation emerges from Riemannian gradient flow on a learned latent manifold. The learned metric encodes representational constraints and computational preferences, while anisotropies in the geometry naturally generate multiple timescales of behaviour, yielding both rapid reactive responses and slower adaptive dynamics without explicit memory modules or recurrent mechanisms. We instantiate this framework through Riemannian representation and dynamics models and evaluate them in partially observable reinforcement-learning environments. Across observation masking, sensory blackouts, dynamics perturbations, and predictive latent-modelling tasks, the proposed approach consistently outperforms feedforward baselines, achieves robustness comparable to recurrent architectures, and produces highly predictable latent trajectories with low long-horizon rollout error. These results suggest that learned latent geometry can serve simultaneously as a substrate for representation, memory, adaptation, and prediction. More broadly, the framework provides a principled connection between dynamical systems, representation learning, and world-model-based intelligence.