Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions

Abstract

Connection, torsion and curvature are introduced for general (local) Leibniz algebroids. Generalized Bismut connection on $TM \oplus \Lambda^{p} T^{\ast}M$ is an example leading to a scalar curvature of the form $R + H^2$ for a closed $(p+2)$-form $H$.