Immersions of Riemannian manifolds with a given normal bundle structure. I
Oldřich Kowalski (1969)
Czechoslovak Mathematical Journal
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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...