The geometry of a physical space is a key ingredient underlying many exotic quantum phenomena. However, accessing physical spaces with non-trivial geometries and many associated unique phenomena are often impeded by experimental constraints. Here, we realize a Bose-Einstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux, topologically equivalent to a two-dimensional (2D) Hall ribbon with two edges connected. This cylindrical surface comprises a real spatial dimension and a curved synthetic dimension formed by cyclically-coupled spin states. The BEC on such a Hall cylinder has counterintuitive properties unattainable by its counterparts in 2D planes. It develops a crystalline order with a nonsymmorphic symmetry and the period of its density modulation halves the lattice spacing. Bloch oscillations of the BEC in the momentum space double the period of the band structure, analogous to traveling on a Mobius strip. Our work opens the door to engineering synthetic curved spaces and observing intriguing quantum phenomena inherent to the topology of spaces.