  In this paper, curved fronts are constructed for spatially periodic bistable
reaction-diffusion equations under the a priori assumption that there exist
pulsating fronts in every direction. Some sufficient and some necessary
conditions of the existence of curved fronts are given. Furthermore, the curved
front is proved to be unique and stable. Finally, a curved front with varying
interfaces is also constructed. Despite the effect of the spatial
heterogeneity, the result shows the existence of curved fronts for spatially
periodic bistable reaction-diffusion equations which is known for the
homogeneous case.
