On the Theory of Gravitational Field in Finsler Spaces ‐ III

From the vector bundle‐like standpoint, the Finslerian gravitational field is regarded as the total space of the vector bundle whose fibre is the internal ( y )‐field spanned by vectors { y } (i.e., the so‐called internal space spanned by { y }) and whose base is the external ( x )‐field spanned by points { x } (i.e., the Einstein's gravitational field). Along this line, in this paper, different from a previous paper [1], the so‐called mapping process of the ( y )‐field on the ( x )‐field is not taken into account and following Miron's method [2, 3], the Finslerian field equations will be derived from the Einstein's field equation for the total space. Some physical considerations will be made on those field equations.