Generalized Lagrange metric derived from a Finsler function (Q1198537)

In two previous papers [Tensor, New Ser. 48, No. 1, 52-63 (1989; Zbl 0703.53021), ibid. No. 2, 153-168 (1989; Zbl 0708.53057)] the authors have studied the generalized metric \(\gamma_{ij}(x)+(1/c^ 2)y_ iy_ j\) derived from a Riemann metric \(\gamma_{ij}(x)\), which can give an interesting geometrical model for gravitation and electromagnetism. The natural extension of this theory consists of the consideration of a general metric \(\gamma_{ij}(x,y)+(1/c^ 2)y_ iy_ j\), where \(\gamma_{ij}(x,y)\) plays the role of the fundamental tensor field of a Finsler space. In this way a generalized Lagrange space is obtained. In the present paper the authors study the geometrical properties of generalized Lagrange spaces based on the above mentioned metrics, their Einstein equations and the properties of the conservation of the energy- moment tensor field.