Geodesic
Flow prolongation of some tangent valued forms
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 493-504.

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We study the prolongation of semibasic projectable tangent valued $k$-forms on fibered manifolds with respect to a bundle functor $F$ on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear $r$-th order connection on the base manifold, where $r$ is the base order of $F$. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued $k$-forms in the case $F$ is a fiber product preserving bundle functor on the category of fibered manifolds with $m$-dimensional bases and local diffeomorphisms as base maps.
Classification : 53C05, 58A20
Keywords: semibasic tangent valued $k$-form; Frölicher-Nijenhuis bracket; bundle functor; flow prolongation of vector fields; connection; curvature 
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     author = {Cabras, Antonella and Kol\'a\v{r}, Ivan},
     title = {Flow prolongation of some tangent valued forms},
     journal = {Czechoslovak Mathematical Journal},
     pages = {493--504},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
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     zbl = {1174.53312},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a14/}
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Cabras, Antonella; Kolář, Ivan. Flow prolongation of some tangent valued forms. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 493-504. http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a14/