On lifts of projectable-projectable classical linear connections to the cotangent bundle

Anna Bednarska

Anna Bednarska

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 67 (2013), / Harvested from The Polish Digital Mathematics Library

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Résumé

We describe all $ℱ^{2} ℳ_{m_{1}, m_{2}, n_{1}, n_{2}}$ -natural operators $D : Q_{p r o j - p r o j}^{τ} ⇝ Q T^{*}$ transforming projectable-projectable classical torsion-free linear connections $\nabla$ on fibred-fibred manifolds $Y$ into classical linear connections $D (\nabla)$ on cotangent bundles $T^{*} Y$ of $Y$ . We show that this problem can be reduced to finding $ℱ^{2} ℳ_{m_{1}, m_{2}, n_{1}, n_{2}}$ -natural operators $D : Q_{p r o j - p r o j}^{τ} ⇝ (T^{*}, \otimes^{p} T^{*} \otimes \otimes^{q} T)$ for $p = 2$ , $q = 1$ and $p = 3$ , $q = 0$ .

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:289731

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     author = {Anna Bednarska},
     title = {On lifts of projectable-projectable classical linear connections to the cotangent bundle},
     journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
     volume = {67},
     year = {2013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2013_67_1_1-10}
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Anna Bednarska. On lifts of projectable-projectable classical linear connections to the cotangent bundle. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 67 (2013) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2013_67_1_1-10/

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