On the partial parallelizable manifolds and associated invariants

Our idea is to use the global diffeomorphism group G (M) to study certain properties of differentiable manifolds endowed with global vector fields. We define a partial parallelizable manifold (p.p.m.) as a couple (M, ρ_p), where ρ_p is a global partial frame (g.p.f.) of the tangent bundle T M of M. In this text there are studied properties of the p.p.m. Certain specific invariants for these manifolds, relative to the group G (M) of the global diffeomorphisms of M, are constructed. We also give some applications and examples. We obtain that a G (M) -invariant [M × ℝ^p] of partial parallelizable manifold (M, ρ_p) is an equivalence class defined by action group G (M) on M.