We semiclassically quantize static topological solitons which exist within a continuum Heisenberg model of an antiferromagnet on an infinite rigid cylinder. It is shown that the energy of a quantized fundamental soliton and the spin-wave spectrum are strongly dependent on the geometry of isotropic spin systems. This dependence implies that the spin-wave gap increases and the energy of a quantized soliton decreases as the radius of the cylinder decreases. Our calculations may have relevance for the recently synthesized carbon nanotubes or cylindrically wrapped thin films of magnetic materials with antiferromagnetic order.
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