Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On curves with nonnegative torsion   We provide new results and new proofs of results about the torsion of curves
in $\mathbb{R}^3$. Let $\gamma$ be a smooth curve in $\mathbb{R}^3$ that is the
graph over a simple closed curve in $\mathbb{R}^2$ with positive curvature. We
give a new proof that if $\gamma$ has nonnegative (or nonpositive) torsion,
then $\gamma$ has zero torsion and hence lies in a plane. Additionally, we
prove the new result that a simple closed plane curve, without any assumption
on its curvature, cannot be perturbed to a closed space curve of constant
nonzero torsion. We also prove similar statements for curves in Lorentzian
$\mathbb{R}^{2,1}$ which are related to important open questions about time
flat surfaces in spacetimes and mass in general relativity.

6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat