Abstract
This paper deals with the Lagrange vertical structure on the vertical tangent space TV (N) endowed with a non-zero (1,1) tensor field F-v satisfying (F-v(2) - a(2))(F-v(2) + a(2))(F-v(2) - b(2))(F-v(2) + b(2)) = 0. The similar structure on the horizontal subspace T-H(N) and on T(N) is investigated if the F(+/- a(2), +/- b(2))-structure on T-V (N) is given. Furthermore, we have proved some theorems and obtained conditions under which the distribution P and Q are del-parallel, (del) over bar anti half parallel when del = (del) over bar. Finally, certain theorems on geodesics on the Lagrange manifold are established.