The natural transformations between r-tangent and r-cotangent bundles over Riemannian manifolds
Jan Kurek ; Włodzimierz M. Mikulski
Annales UMCS, Mathematica, Tome 68 (2015), / Harvested from The Polish Digital Mathematics Library
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If (M,g) is a Riemannian manifold, we have the well-known base preserving vector bundle isomorphism TM ≅ T∗ M given by υ → g(υ,−) between the tangent TM and the cotangent T∗ M bundles of M. In the present note, we generalize this isomorphism to the one T(r)M ≅ Tr∗ M between the r-th order vector tangent T(r)M = (Jr(M,R)0)∗ and the r-th order cotangent Tr∗ M = Jr(M,R)0 bundles of M. Next, we describe all base preserving vector bundle maps CM(g) : T(r)M → Tr∗ M depending on a Riemannian metric g in terms of natural (in g) tensor fields on M.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:270006 
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     author = {Jan Kurek and W\l odzimierz M. Mikulski},
     title = {The natural transformations between r-tangent and r-cotangent bundles over Riemannian manifolds},
     journal = {Annales UMCS, Mathematica},
     volume = {68},
     year = {2015},
     zbl = {1312.58003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0006}
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Jan Kurek; Włodzimierz M. Mikulski. The natural transformations between r-tangent and r-cotangent bundles over Riemannian manifolds. Annales UMCS, Mathematica, Tome 68 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0006/

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