%0 Journal Article
%T On curves with nonnegative torsion
%A Hubert L. Bray
%A Jeffrey L. Jauregui
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1312.5171v2