Symplectic structures on the tangent bundle of a smooth manifold

Abouqateb Abdelhak, Mohamed Boucetta, Aziz Ikemakhen

We give a method to lift $(2,0)$-tensors fields on a manifold $M$ to build symplectic forms on $TM$. Conversely, we show that any symplectic form $\Om$ on $TM$ is symplectomorphic,…