  We study the surface resistivity of a three-dimensional topological insulator
when the boundaries exhibit a non trivial curvature. We obtain an analytical
solution for a spherical topological insulator, and we show that a non trivial
quantum spin connection emerges from the three dimensional band structure. We
analyze the effect of the spin connection on the scattering by a bump on a flat
surface. Quantum effects induced by the geometry lead to resonances when the
electron wavelength is comparable to the size of the bump.
