The natural transformations between r-tangent and r-cotangent bundles over Riemannian manifolds
Jan Kurek, Włodzimierz Mikulski (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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If is a Riemannian manifold, we have the well-known base preserving vector bundle isomorphism given by between the tangent and the cotangent bundles of . In the present note, we generalize this isomorphism to the one between the -th order vector tangent and the -th order cotangent bundles of . Next, we describe all base preserving vector bundle maps depending on a Riemannian metric in terms of natural (in ) tensor fields on .