  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, in a neighborhood of the zero section, to a
symplectic form built naturally from three $(2,0)$-tensor fields associated to
$\Om$.
