A geometry for Lagrangians on the bundle R^n x T^1_n M

Abstract

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.

Keywords

• connections
• semisprays
• jets
• lagrangians