The Bianchi identity is a differential equation satisfied by curvature data. It can be thought of as generalizing the equation for a real-valued 1-form to higher degree and nonabelian forms. Generally it applies to the curvature of ∞-Lie algebroid valued differential forms. Let be a smooth manifold. For a differential 1-form, its curvature 2-form is the de Rham differential . The Bianchi identity in this case is the equation More generally, for an arbitrary Lie algebra and a Lie-algebra valued..