On natural vector bundle morphisms over
Some properties and applications of natural vector bundle morphisms over are presented.
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 lifts of higher order of multiplicative Dirac structures
The tangent lifts of higher order of Dirac structures and some properties have been defined in [9] and studied in [11]. By the same way, the tangent lifts of higher order of Poisson structures have been studied in [10] and some applications are given. In particular, the authors have studied the nature of the Lie algebroids and singular foliations induced by these lifting. In this paper, we study the tangent lifts of higher order of multiplicative Poisson structures, multiplicative Dirac structures...
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.
On lifts of some projectable vector fields associated to a product preserving gauge bundle functor on vector bundles
For a product preserving gauge bundle functor on vector bundles, we present some lifts of smooth functions that are constant or linear on fibers, and some lifts of projectable vector fields that are vector bundle morphisms.
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...
Some further results on lifts of linear vector fields related to product preserving gauge bundle functors on vector bundles
We present some lifts (associated to a product preserving gauge bundle functor on vector bundles) of sections of the dual bundle of a vector bundle, some derivations and linear connections on vector bundles.
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