The natural transformations between r-th order prolongation of tangent and cotangent bundles over Riemannian manifolds

Mariusz Plaszczyk


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 → JrT*M between the r-th order prolongation JrTM of tangent TM and the r-th order prolongation JrT*M of cotangent T*M 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.


Riemannian manifold; higher order prolongation of a vector bundle; natural tensor; natural operator

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Data publikacji: 2015-11-30 09:21:12
Data złożenia artykułu: 2015-09-03 12:56:40


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