Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rotations with Constant Curl are Constant   It is a classical result that if $u \in C^2(\mathbb{R}^n;\mathbb{R}^n)$ and
$\nabla u \in SO(n)$ it follows that $u$ is rigid. In this article this result
is generalized to matrix fields with non-vanishing curl. It is shown that every
matrix field $R\in C^2(\Omega \subseteq \mathbb{R}^3;SO(3))$ such that
$\operatorname{curl } R = constant$ is necessarily constant. Moreover, it is
proved in arbitrary dimensions that a measurable rotation field is as regular
as its distributional curl allows. In particular, a measurable matrix field $R:
\Omega \to SO(n)$, whose curl in the sense of distributions is smooth, is also
smooth.

10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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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: supr-con