Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic structures on the tangent bundle of a smooth manifold   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
$\Om$.

36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con