Frölicher–Nijenhuis bracket
In mathematics, the Frölicher–Nijenhuis bracket is an extension of the Lie bracket of vector fields to vector-valued differential forms on a differentiable manifold. It is useful in the study of connections, notably the Ehresmann connection, as well as in the more general study of projections in the tangent bundle.
Source: Wikipedia — Frölicher–Nijenhuis bracket (CC BY-SA 4.0)