On the Metric Structures and Connection Considerations of Gravitational Field in Finsler Spaces

In this paper, some physico-geometrical considerations are developed on the concept of nonlocal field theory associated with the Finslerian gravitational field. In particular, the nonlocalization by the internal variable at the more higher-order level or the more microscopic level than the Finslerian one is considered in detail. An application of the metric structure of Friedmann - Robertson - Walker - model (FRW) is also given in the framework of the vector bundle.