On the theory of gravitational field in Finsler spaces

Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as gλκ(x, y) = γλκ(x) + hλκ(x, y) is proposed, where γλκ denotes the Riemann metric of Einstein's gravitational field, while hλκ the Finsler metric induced by the Riemann metric hij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as y-bari = Kji(x, y) yj in the internal field, is grasped by the Finslerian parallelism δyi (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δyκ = eiκ(x) δyi. The whole metrical Finsler connection D for gλκ (i.e., Dgλκ = 0) is determined by taking account of the intrinsic behaviour δyκ. (author)