On connections associated with a finslerian gravitational field

Some modified connections associated with a Finslerian gravitational field are considered y reducing or extending the set of independent variables (xk, yi) (k, i=1, 2, 3, 4) (yi—vector) in various ways. The following five examples are considered: (xk, yi) are restricted to (xk, y0) (y0—scalar) or (x0, yi) (x0—time axis); (xk, yi) are extended to (xk, yi, Pi) (pi—covector dual to yi) or (xk, yi, qa) (qa—arbitrary covector, a=1, 2, 3, 4); (xk, yi) are extended to (xk, y(α)i), (y(α)—α-th nonvector variable, α=1,2,…, m).