(i) In gravitation theory on a world manifold X , one can always choose an atlas of a frame bundle F X (characterized by local frame fields { h λ λ } ) with S O ( 3 ) -valued transition functions. These transition functions preserve a time-like component h 0 = h 0 μ μ ∂ ∂ μ μ of local frame fields which, therefore, is globally defined. It is a nowhere vanishing vector field on X . Accordingly, the dual time-like covector field h 0 = h λ λ 0 d x λ λ also is globally defined, and it yields a spatial distribution F ⊂ ⊂ T X on X such that h 0 ⌋ ⌋ F = 0 . Then the tangent bundle T X of a world manifold X admits a space-time decomposition T X = F ⊕ ⊕ T 0 X , where T 0 X is a one-dimensional fibre bundle spanned by a time-like vector field h 0 . This decomposition, is called the g -compatible space-time structure. It makes a world manifold the space-time.