  Classical Heisenberg spins in the continuum limit (i.e. the nonlinear
sigma-model) are studied on an elastic cylinder section with homogeneous
boundary conditions. The latter may serve as a physical realization of
magnetically coated microtubules and cylindrical membranes. The corresponding
rigid cylinder model exhibits topological soliton configurations with
geometrical frustration due to the finite length of the cylinder section.
Assuming small and smooth deformations allows to find shapes of the elastic
support by relaxing the rigidity constraint: an inhomogeneous Lam\'e equation
arises. Finally, this leads to a novel geometric effect: a global shrinking of
the cylinder section with swellings.
