On Generalized Lagrange Spaces and Corresponding Lagrange Spaces Arising from a Generalized Finsler Space

The purpose of the present paper is to study the geometrical properties of a generalized Lagrange space L_n with metric L_gij (x,y) = g_ij (x,y)+(1/c²)y_iy_j and to find the relations among metric tensors, angular metric tensors, Cartan tensors of generalized Lagrange space L_n, corresponding Lagrange space L*_n, generalized Finsler space F_n and associated Finsler space F*_n, where g_ij (x,y) be metric tensor of a generalized Finsler space and y_i = g_ij (x,y)y^j. Moreover the concept of C-reducibility has been introduced in Lagrange and generalized Lagrange spaces.