Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riemannian Curl in Contact Geometry   We consider a contact manifold with a pseudo-Riemannian metric and define a
contact vector field intrinsically associated to this pair of structures. We
call this new differential invariant the contact Riemannian curl. On a
Riemannian manifold, Killing vector fields are those that annihilate the
metric; a Killing $1$-form is obtained from a Killing vector field by lowering
indices. We show that the contact Riemannian curl vanishes if the metric is of
constant curvature and the contact structure is defined by a Killing $1$-form.
We also show that the contact Riemannian curl has a strong similarity with the
Schwarzian derivative since it depends only on the projective equivalence class
of the metric. For the Laplace-Beltrami operator on a contact manifold, the
contact Riemannian curl is proportional to the subsymbol defined in
arXiv:1205.6562. We also show that the contact Riemannian curl vanishes on the
(co)tangent bundle over a Riemannian manifold. This implies that the
corresponding subsymbol of the Laplace-Beltrami operator is identically zero.

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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci