Cognitive brain functions rely on experience-dependent internal representations of relevant information. Such representations are organized by attractor dynamics or other mechanisms that constrain population activity onto 'neural manifolds'. Quantitative analyses of representational manifolds are complicated by their potentially complex geometry, particularly in the absence of attractor states. Here we trained juvenile and adult zebrafish in an odor discrimination task and measured neuronal population activity to analyze representations of behaviorally relevant odors in telencephalic area pDp, the homolog of piriform cortex. No obvious signatures of attractor dynamics were detected. However, olfactory discrimination training selectively enhanced the separation of neural manifolds representing task-relevant odors from other representations, consistent with predictions of autoassociative network models endowed with precise synaptic balance. Analytical approaches using the framework of manifold capacity revealed multiple geometrical modifications of representational manifolds that supported the classification of task-relevant sensory information. Manifold capacity predicted odor discrimination across individuals better than other descriptors of population activity, indicating a close link between manifold geometry and behavior. Hence, pDp and possibly related recurrent networks store information in the geometry of representational manifolds, resulting in joint sensory and semantic maps that may support distributed learning processes.