Very special relativity in curved space-times

The generalization of Cohen and Glashow's very special relativity to curved space-times is considered. Gauging the SIM(2) symmetry does not, in general, provide the coupling to the gravitational background. However, locally SIM(2) invariant Lagrangians can always be constructed. For space-times with SIM(2) holonomy, they describe chiral fermions propagating freely as massive particles.