Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic sections of tangent bundles equipped with Riemannian
  $g$-natural metrics   Let $(M,g)$ be a Riemannian manifold. When $M$ is compact and the tangent
bundle $TM$ is equipped with the Sasaki metric $g^s$, the only vector fields
which define harmonic maps from $(M,g)$ to $(TM,g^s)$, are the parallel ones.
The Sasaki metric, and other well known Riemannian metrics on $TM$, are
particular examples of $g$-natural metrics. We equip $TM$ with an arbitrary
Riemannian $g$-natural metric $G$, and investigate the harmonicity of a vector
field $V$ of $M$, thought as a map from $(M,g)$ to $(TM,G)$. We then apply this
study to the Reeb vector field and, in particular, to Hopf vector fields on
odd-dimensional spheres.

33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc