The Natural Operators Similar to the Twisted Courant Bracket One

Given natural numbers m3 and p3, all Mfm-natural operators AH sending p-forms Hp(M) on m-manifolds M into bilinear operators AH:(X(M)1(M) transforming pairs of couples of vector fields and 1-forms on M into couples of vector fields and 1-forms on M are founded. If m3 and p3, then that any (similar as above) Mfm-natural operator A which is defined only for closed p-forms H can be extended uniquely to the one A which is defined for all p-forms H is observed. If p=3 and m3, all Mfm-natural operators A (as above) such that AH satisfies the Leibniz rule for all closed 3-forms H on m-manifolds M are extracted. The twisted Courant bracket [-,-]H for all closed 3-forms H on m-manifolds M gives the most important example of such Mfm-natural operator A.