Bonnet surfaces in (2 + 1)-dimensional stationary spacetimes

In this paper, we primarily employ the moving frame method to establish an existence theorem for spacelike Bonnet surfaces in stationary Lorentzian three-manifolds L3. These results characterize the extrinsic geometric rigidity of Bonnet surfaces. Furthermore, such surfaces offer potential applications to the related studies of initial spacelike hypersurfaces in (2 + 1)-dimensional gravity, serving as promising candidates for preferred foliations.