Deviation Equations of Synge and Schild over (l N , G)-spaces

Deviation equation of Synge and Schild has been investigated over dif-ferentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metric [(Ln, g)-spaces]. It is shown that the condition £ ξ u = 0 for obtaining this equation is only a sufficient (but not necessary) condition. By means of a non-isotropic (non-null) vector field u [g(u, u) = e = 0] and the metric hu, orthogonal to it, a projected deviation equation of Synge and Schild has been obtained for the orthogonal to u vector field ξ ⊥ and its square L 2 = g(ξ ⊥ , ξ ⊥). For a given non-isotropic, auto-parallel and normalized vector field u this equation could have some simple solutions.