Displaying similar documents to “The natural transformations between r-th order prolongation of tangent and cotangent bundles over Riemannian manifolds”

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

Mariusz Plaszczyk (2015)

Annales UMCS, Mathematica

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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...

The natural transformations between r-tangent and r-cotangent bundles over Riemannian manifolds

Jan Kurek, Włodzimierz M. Mikulski (2015)

Annales UMCS, Mathematica

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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...

On natural metrics on tangent bundles of Riemannian manifolds

Mohamed Tahar Kadaoui Abbassi, Maâti Sarih (2005)

Archivum Mathematicum

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There is a class of metrics on the tangent bundle T M of a Riemannian manifold ( M , g ) (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric g [Kow-Sek1]. We call them “ g -natural metrics" on T M . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on T M from some quadratic forms on O M × ℝ m to find metrics (not necessary...