Tangential curvatures are a key geometric feature of tissue folds in the human cerebral cortex. In the brain, these smoother and firmer bends are called gyri and sulci and form distinctive curved tissue patterns imposing a mechanical stimulus on neuronal networks. This stimulus is hypothesized to be essential for proper brain cell function but lacks in most standard neuronal cell assays. A variety of soft lithographic micropatterning techniques can be used to integrate round geometries in cell assays. Most microfabricated patterns, however, focus only on a small set of defined curvatures. In contrast, curvatures in the brain span a wide physical range, leaving it unknown which precise role distinct curvatures may play on neuronal cell signaling. Here we report a hydrogel-based multi-curvature design consisting of over twenty bands of distinct parallel curvature ranges to precisely engineer neuronal networks' growth and signaling under patterns of arcs. Monitoring calcium and mitochondrial dynamics in primary rodent neurons grown over two weeks in the multi-curvature patterns, we found that static calcium signaling was locally attenuated under higher curvatures (k > 0.01 μm-1). In contrast, to randomize growth, transient calcium signaling showed higher synchronicity when neurons formed networks in confined multi-curvature patterns. Additionally, we found that mitochondria showed lower motility under high curvatures (k > 0.01 μm-1) than under lower curvatures (k < 0.01 μm-1). Our results demonstrate how sensitive neuronal cell function may be linked and controlled through specific curved geometric features. Furthermore, the hydrogel-based multi-curvature design possesses high compatibility with various surfaces, allowing a flexible integration of geometric features into next-generation neuro devices, cell assays, tissue engineering, and implants.