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- W2955521711 abstract "Given natural numbers $$mge 3$$ and $$pge 3$$ , all $$mathcal {M} f_m$$ -natural operators $$A_{H}$$ sending p-forms $$Hin Omega ^p(M)$$ on m-manifolds M into bilinear operators $$A_H:(mathcal {X}(M),oplus ,Omega ^1(M))times (mathcal {X}(M),oplus ,Omega ^1(M))rightarrow mathcal {X}(M),oplus ,Omega ^1(M)$$ 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 $$mge 3$$ and $$pge 3$$ , then that any (similar as above) $$mathcal {M} f_m$$ -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 $$mge 3$$ , all $$mathcal {M} f_m$$ -natural operators A (as above) such that $$A_H$$ 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 $$mathcal {M} f_m$$ -natural operator A." @default.
- W2955521711 created "2019-07-12" @default.
- W2955521711 creator A5016408156 @default.
- W2955521711 date "2019-06-24" @default.
- W2955521711 modified "2023-09-24" @default.
- W2955521711 title "The Natural Operators Similar to the Twisted Courant Bracket One" @default.
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- W2955521711 doi "https://doi.org/10.1007/s00009-019-1367-1" @default.
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