The distribution D of an almost contact metric structure (ϕ, ξ, η, g) is an odd analogue of the tangent bundle. In the paper an intrinsic symplectic structure naturally associated with the initial almost contact metric structure is constructed. The interior connection defines the parallel transport of admissible vectors (i.e. vectors belonging to the distribution D) along admissible curves. Each corresponding extended connection is a connection in the vector bundle (D, π,X) defined by the interior connection and by an endomorphism N : D → D.
