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This article is concerned with some geometric structures of the jetbundle IR^n ×T ^1_nM, modelled by the non autonomous tangent bundle geometry. We use this fact to construct similar objects like a particular family of vector fields and we study its relationship with a tensor field IK, which defines a type of Ehresmann connection. The integration of the system of partial differential equations associated to IK is then accomplished via the integration of the corresponding Euler-Lagrange equations for a regular Lagrangian defined on this jet bundle.