Algèbre de Lie attachée à la structure presque-tangente. (The Lie algebra associated to an almost tangent structure) (Q1089931)

Let M be an n-dimensional differentiable manifold and TM its tangent bundle. Let J denote the canonical almost tangent structure on TM. The author studies the properties of the Lie algebra \(L_ M\) of infinitesimal automorphisms of (TM,J), that is, \(L_ M=\{A\in X(TM)| L_ AJ=0\}.\) The following result is proved: Let M and N be two connected and paracompact differentiable manifolds; if the Lie algebras \(L_ M\) and \(L_ N\) are isomorphic, then M and N are diffeomorphic.