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If \(m\geq p+1\geq 2\) (or \(m=p\geq 3\)), 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.
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2018
online
2018-12-22
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Bibliografia
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- Doupovec, M., Kurek, J., Mikulski, W. M., The natural brackets on couples of vector fields and 1-forms, Turkish J. Math. 42 (4) (2018), 1853-1862.
- Dębecki, J., Linear liftings of skew symmetric tensor fields of type (1,2) to Weil bundles, Czechoslovak Math. J. 60(135) (4) (2010), 933-943.
- Gualtieri, M., Generalized complex geometry, Ann. of Math. (2) 174 (1) (2011), 75-123.
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- Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
- Kurek, J., Mikulski, W. M., The natural linear operators \(T^*\rightsquigarrow TT^{(r)}\), Colloq. Math. 95 (1) (2003), 37-47.
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Bibliografia
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bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_29