Geodesic
Lifts of Poisson–Nijenhuis Structures to Weil Bundles
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 203-214

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In the present paper we show that the complete lifts of the structure tensors $P$ and $N$ of a Poisson–Nijenhuis manifold $(M,P,N)$ to the Weil bundle $T^\mathbb AM$ induce a structure of Poisson–Nijenhuis manifold on $T^\mathbb AM$. We compute the modular vector fields of this manifold.
Keywords: Poisson–Nijenhuis manifold, modular class, Weil bundle, complete lift, vertical lift.
Mots-clés : Weil algebra 
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     author = {V. V. Shurygin (jr.)},
     title = {Lifts of {Poisson{\textendash}Nijenhuis} {Structures} to {Weil} {Bundles}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {203--214},
     publisher = {mathdoc},
     volume = {151},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a18/}
}
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V. V. Shurygin (jr.). Lifts of Poisson–Nijenhuis Structures to Weil Bundles. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 203-214. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a18/