The natural transformations between T-th order prolongation of tangent and cotangent bundles over Riemannian manifolds
Mariusz Plaszczyk
Annales UMCS, Mathematica, Tome 68 (2015), p. 91-108 / Harvested from The Polish Digital Mathematics Library
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If (M,g) is a Riemannian manifold then there is the well-known base preserving vector bundle isomorphism TM → T* M given by v → g(v,−) between the tangent TM and the cotangent T* M bundles of M. In the present note first we generalize this isomorphism to the one JrTM → JrTM between the r-th order prolongation JrTM of tangent TM and the r-th order prolongation JrT M of cotangent TM bundles of M. Further we describe all base preserving vector bundle maps DM(g) : JrTM → JrT* 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:270870 
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     author = {Mariusz Plaszczyk},
     title = {The natural transformations between T-th order prolongation of tangent and cotangent bundles over Riemannian manifolds},
     journal = {Annales UMCS, Mathematica},
     volume = {68},
     year = {2015},
     pages = {91-108},
     zbl = {1321.58002},
     language = {en},
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Mariusz Plaszczyk. The natural transformations between T-th order prolongation of tangent and cotangent bundles over Riemannian manifolds. Annales UMCS, Mathematica, Tome 68 (2015) pp. 91-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0015/

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