Geodesic
On the Courant bracket on couples of vector fields and \(p\)-forms
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 72 (2018) no. 2.

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If m≥ p+1≥ 2 (or m=p≥ 3), all  natural bilinear  operators A transforming pairs of couples of vector fields and p-forms on m-manifolds M into couples of vector fields and p-forms on M are described. It is observed that  any natural skew-symmetric bilinear operator A as above coincides with the generalized Courant bracket up to three (two, respectively) real constants.
Keywords: Natural operator, vector field, p-form 
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Doupovec, Miroslav; Kurek, Jan; Mikulski, Włodzimierz. On the Courant bracket on couples of vector fields and \(p\)-forms. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 72 (2018) no. 2. http://geodesic.mathdoc.fr/item/AUM_2018_72_2_a3/

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