Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contact structures and Beltrami fields on the torus and the sphere   We present new explicit tight and overtwisted contact structures on the
(round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly
compatible. Our proofs are based on the construction of nonvanishing curl
eigenfields using suitable families of Jacobi or trigonometric polynomials. As
a consequence, we show that the contact sphere theorem of Etnyre, Komendarczyk
and Massot (2012) does not hold for weakly compatible metric as it was
conjectured. We also establish a geometric rigidity for tight contact
structures by showing that any contact form on the 3-sphere admitting a
compatible metric that is the round one is isometric, up to a constant factor,
to the standard (tight) contact form.

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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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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: funct-an
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The categories of this paper are: nlin