Leibniz algebroids, generalized Bismut connections and Einstein–Hilbert actions

Connection, torsion and curvature are introduced for general (local) Leibniz algebroids. Generalized Bismut connection on TM⊕ΛpT∗MTM⊕ΛpT∗M is an example leading to a scalar curvature of the form R+H2R+H2 for a closed (p+2)(p+2)-form HH.