Heisenberg spins on a cylinder section

Classical Heisenberg spins in the continuum limit (i.e. the nonlinear sigma -model) are studied on an elastic cylinder section with homogeneous bounda ry conditions. The latter may serve as a physical realization of magnetical ly coated microtubules and cylindrical membranes. The corresponding rigid c ylinder model exhibits topological soliton configurations with geometrical frustration due to the finite length of the cylinder section. Assuming smal l and smooth deformations allows to find shapes of the elastic support by r elaxing the rigidity constraint: an inhomogeneous Lame equation arises. Fin ally, this leads to a novel geometric effect: a global shrinking of the cyl inder section with swellings.