Immersions of Riemannian manifolds with a given normal bundle structure. I
Oldřich Kowalski (1969)
Czechoslovak Mathematical Journal
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Oldřich Kowalski (1969)
Czechoslovak Mathematical Journal
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(1972)
Collectanea Mathematica
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Werner H. Greub (1977)
Collectanea Mathematica
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Peter B. Gilkey, John V. Leahy, Jeong Hyeong Park (1997)
Zbornik Radova
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Manoharan, P. (2002)
International Journal of Mathematics and Mathematical Sciences
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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...
Janyška, Josef
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