It is shown that the action associated with center vortices in SU(2) lattice
gauge theory is strongly correlated with extrinsic and internal curvatures of
the vortex surface and that this correlation persists in the continuum limit.
Thus a good approximation for the effective vortex action is the action of
rigid strings, which can reproduce some of the observed geometric properties of
center vortices. It is conjectured that rigidity may be induced by some fields
localized on vortices, and a model-independent test of localization is
performed. Monopoles detected in the Abelian projection are discussed as
natural candidates for such two-dimensional fields.Comment: 7 pages, 8 figures, RevTeX