Displaying similar documents to “On lifts of some projectable vector fields associated to a product preserving gauge bundle functor on vector bundles”

On the geometry of vertical Weil bundles

Ivan Kolář (2014)

Archivum Mathematicum

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We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections.

On the natural transformations of Weil bundles

Ivan Kolář (2013)

Archivum Mathematicum

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First we deduce some general results on the covariant form of the natural transformations of Weil functors. Then we discuss several geometric properties of these transformations, special attention being paid to vector bundles and principal bundles.

On the Weilian prolongations of natural bundles

Ivan Kolář (2012)

Czechoslovak Mathematical Journal

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We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration F ( E M ) of two natural bundles E and F . Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem.

The natural affinors on some fiber product preserving gauge bundle functors of vector bundles

Jan Kurek, Włodzimierz M. Mikulski (2006)

Archivum Mathematicum

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We classify all natural affinors on vertical fiber product preserving gauge bundle functors F on vector bundles. We explain this result for some more known such F . We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor F * dual to F as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.

Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.

Wlodzimierz M. Mikulski (2006)

Extracta Mathematicae

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Let A be a Weil algebra and V be an A-module with dim V < ∞. Let E → M be a vector bundle and let TE → TM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form Tφ : T E → ΛT*TM ⊗ TTE on TE → TM from a linear semibasic tangent valued p-form φ : E → ΛT*M ⊗­ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[Tφ, Tψ]] = T ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and ψ on E → M. We apply...