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Horizontal lift of tensor fields of type (1,1) from a manifold to its tangent bundle of higher order

Gancarzewicz, Jacek; Mahi, Salima; Rahmani, Noureddine — 1987

Proceedings of the 14th Winter School on Abstract Analysis

Connections of higher order and product preserving functors

Jacek Gancarzewicz; Noureddine Rahmani; Modesto R. Salgado — 2002

Czechoslovak Mathematical Journal

In this paper we consider a product preserving functor $ℱ$ of order $r$ and a connection $Γ$ of order $r$ on a manifold $M$ . We introduce horizontal lifts of tensor fields and linear connections from $M$ to $ℱ (M)$ with respect to $Γ$ . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.

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