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Connection, torsion and curvature are introduced for general (local) Leibnizalgebroids. 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 $H$.

Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions