  We consider a curved chain of nonlinear oscillators and show that the
interplay of curvature and nonlinearity leads to a symmetry breaking when an
asymmetric stationary state becomes energetically more favorable than a
symmetric stationary state. We show that the energy of localized states
decreases with increasing curvature, i.e. bending is a trap for nonlinear
excitations. A violation of the Vakhitov-Kolokolov stability criterium is found
in the case where the instability is due to the softening of the Peierls
internal mode.
