  We construct a general theory of adiabatic propagation of spinor
exciton-polaritons in waveguides of arbitrary shape, accounting for the effects
of TE-TM splitting in linear polarizations and Zeeman splitting in circular
polarizations. The developed theory is applied for the description of
waveguides of periodically curved shape. We show that in this geometry the
periodic rotation of the effective in-plane magnetic field produced by TE-TM
interaction results in a nontrivial band-gap structure, which can be
additionally tuned by application of an external magnetic field. It is also
demonstrated, that spin-dependent interactions between polaritons lead to the
formation of stable gap solitons.
