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1-jet spaces abstract physical C2 solutions canonical nonlinear connection Cartan connection Christoffel symbols classical covariant derivatives curvature d-tensor field d-torsions DUMITRU OPRIS dynamical systems Einstein equations Euler-Lagrange equations field theories fluid geodesies geometrical and abstract geometrical context geometrical objects geometrical structure given PDEs system global minimum points harmonic maps inverse problem jet bundle jet fibre bundle jet prolongation jet space least squares Lagrangian least squares multi-time lois de conservation Maxwell and Einstein Maxwell equations mecanique newtonienne metrical multi-time Lagrange MIRON multi-time dependent spray multi-time electromagnetic multi-time gravitational multi-time Lagrange space multi-time least squares Navier-Stokes equations Neagu order PDEs system paper paracompactness PDEs system 1.4 physical fields Poincare problem preceding geometrical probleme inverse produced qualitative result r-order relativistic multi-time Riemannian manifolds Riemannian metric hap solutions of PDEs space of electrodynamics space PDEsEDML squares multi-time Lagrangian system of order Systemes dynamiques Theorem 1.3 Udri§te Udri§te's vector bundle vector field VIRGIL OBADEANU Yang-Mills