Immersions of Riemannian manifolds with a given normal bundle structure. I
Oldřich Kowalski (1969)
Czechoslovak Mathematical Journal
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Displaying similar documents to “ vector bundle valued forms and the Laplace-Beltrami operator”
Immersions of Riemannian manifolds with a given normal bundle structure. I
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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...
Natural 2-forms on the tangent bundle of a Riemannian manifold
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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-th order prolongation of tangent and cotangent bundles over Riemannian manifolds
Mariusz Plaszczyk (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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 → 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...