Cubic interactions of massless higher spins in (A)dS: Metric-like approach

Cubic interactions of higher-spin gauge fields in (A)d_Sd$(A)d{S}_d$ are studied in the metric-like approach. Making use of the traceless and transverse constraints together with the ambient-space formalism, all consistent parity-invariant cubic vertices are obtained for d?4$d?4$ in a closed form pointing out the key role of their flat-space counterparts.