Narrow Results

We construct and give a complete classification of all the differential symmetry breaking operators ${𝔻}_{\lambda ,\nu }^m:C^{\infty }(S^3,{{𝒱}}_{\lambda }^3)\to C^{\infty }(S^2,{{ℒ}}_{m,\nu })$, between the spaces of smooth sections of a vector bundle of rank $3$ over the $3$-sphere ${{𝒱}}_{\lambda }^3\to S^3$, and a line bundle over the $2$-sphere ${{ℒ}}_{m,\nu }\to S^2$. In particular, we give necessary and sufficient conditions on the tuple of parameters $(\lambda ,\nu ,m)$ for which these operators exist.