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Section 1 contains some physical and geometrical aspects of the generalized Lagrangian geometry of physical fields developed by Miron and Anastasiei (7), which represents the start point in our generalized metrical multi-time Lagrangian approach of the theory of physical fields. Section 2 exposes a geometrization of a Kronecker h-regular vertical metrical d-tensor G ()() (i)(j) on the jet fibre bundle of order one J1(T,M). We emphasize that this geometrization gives a mathematical model for both the gravita- tional and electromagnetic field theory, in a general setting. Thus, Section 3 presents the generalized metrical multi-time Lagrange theory of electromagnetism and describes its Maxwell equations. Section 4 presents the Einstein equations which govern the gener- alized metrical multi-time Lagrange theory of gravitational field. The conservation laws of the gravitational field are also described in terms of generalized metrical multi-time Lagrange geometry. Section 5 gives a more natural form of the Einstein equations and of their conservation laws.

Generalized metrical multi-time Lagrange geometry of physical fields