A CHARACTERIZATION OF TANGENT AND STABLE TANGENT-BUNDLES

We apply a result of Nagano to prove that an integrable almost tangent manifold M endowed with a vector field satisfying similar properties to those satisfied by the canonical vector field of a vector bundle admits a unique vector bundle structure such that M is isomorphic to a tangent bundle. Thus we obtain a characterization of tangent bundles. This characterization was obtained by Crampin et al. and Filippo et al, in a different way. We also extend the result to stable tangent bundles. An application to reduction of degenerate autonomous and non-autonomous Lagrangian systems is given.