Recent studies have proposed that neural circuits have a $\textit{task manifold}$: i.e., a subset of the neural state-space to which neural activity is confined as an animal performs a task [1]. Thus, discovering and characterising these manifolds and their associated dynamics from experimental data can shed light on the neural computations unfolding within the brain during various cognitive tasks. Yet, common manifold discovery methods often do not take into account that neural data is generated by an underlying dynamical system. To address this, we first derive a general class of manifolds that neural dynamics can implement. Building on these results, we introduce a dynamical systems-based dimensionality reduction method for neural population data: $\textit{Manifold Discovery via Dynamical Systems}$ (MDDS). We illustrate its usefulness by applying it to recordings of the macaque motor and premotor cortex during a reach task [2] and visual cortex imaging during a perceptual decision making task [3] where we show that MDDS uncovers a manifold with task-relevant geometry. Overall, our framework offers a link between the geometric and dynamical perspectives on population activity, and provides a generative model to uncover task manifolds from neural data.