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The geometry of autonomous metrical multi-time Lagrange space of electrodynamics. (English) Zbl 1011.53053

The author defines the notion of the autonomous metrical multitime Lagrangian space of electrodynamics denoted by \(\text{EDML}^n_p\). Then, he studies the geometry of this structure in the sense of \(d\)-connections, torsion and \(d\)-tensors. Also he gives the generalized Maxwell, Einstein equations and their generalized conservation laws.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C80 Applications of global differential geometry to the sciences
53C40 Global submanifolds
78A25 Electromagnetic theory (general)