Finsler-lagrange spaces with (α, β)-metrics and ingarden spaces

The paper is devoted to the differential geometry of the so called Finsler-Lagrange spaces with (α, β)-metrics. By means of the Lorentz nonlinear connection and canonical metrical connection, the geometry of these spaces can be sufficiently well developed. In particular, if this space is endowed with Lorentz nonlinear connection we obtain the most general concept of Ingarden space. The geometry of these spaces is developed, especially for the theory of electromagnetic field.