New versions of curvature and torsion formulas for the complete lifting of a linear connection to Weil bundles
New versions of Slovák’s formulas expressing the covariant derivative and curvature of the linear connection are presented.
Tangent Dirac structures of higher order
Let be an almost Dirac structure on a manifold . In [2] Theodore James Courant defines the tangent lifting of on and proves that: If is integrable then the tangent lift is also integrable. In this paper, we generalize this lifting to tangent bundle of higher order.
Some properties of tangent Dirac structures of higher order
Let be a smooth manifold. The tangent lift of Dirac structure on was originally studied by T. Courant in [3]. The tangent lift of higher order of Dirac structure on has been studied in [10], where tangent Dirac structure of higher order are described locally. In this paper we give an intrinsic construction of tangent Dirac structure of higher order denoted by and we study some properties of this Dirac structure. In particular, we study the Lie algebroid and the presymplectic foliation...
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