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On curves with nonnegative torsion

Publication ,  Journal Article
Bray, HL; Jauregui, JL
Published in: Archiv der Mathematik
June 29, 2015

We provide new results and new proofs of results about the torsion of curves in $${\mathbb{R}^3}$$R3. Let $${\gamma}$$γ be a smooth curve in $${\mathbb{R}^3}$$R3 that is the graph over a simple closed curve in $${\mathbb{R}^2}$$R2 with positive curvature. We give a new proof that if $${\gamma}$$γ has nonnegative (or nonpositive) torsion, then $${\gamma}$$γ 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 $${\mathbb{R}^{2,1}}$$R2,1 which are related to important open questions about time flat surfaces in spacetimes and mass in general relativity.

Duke Scholars

Published In

Archiv der Mathematik

DOI

EISSN

1420-8938

ISSN

0003-889X

Publication Date

June 29, 2015

Volume

104

Issue

6

Start / End Page

561 / 575

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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MLA
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Bray, H. L., & Jauregui, J. L. (2015). On curves with nonnegative torsion. Archiv Der Mathematik, 104(6), 561–575. https://doi.org/10.1007/s00013-015-0767-0
Bray, H. L., and J. L. Jauregui. “On curves with nonnegative torsion.” Archiv Der Mathematik 104, no. 6 (June 29, 2015): 561–75. https://doi.org/10.1007/s00013-015-0767-0.
Bray HL, Jauregui JL. On curves with nonnegative torsion. Archiv der Mathematik. 2015 Jun 29;104(6):561–75.
Bray, H. L., and J. L. Jauregui. “On curves with nonnegative torsion.” Archiv Der Mathematik, vol. 104, no. 6, June 2015, pp. 561–75. Scopus, doi:10.1007/s00013-015-0767-0.
Bray HL, Jauregui JL. On curves with nonnegative torsion. Archiv der Mathematik. 2015 Jun 29;104(6):561–575.
Journal cover image

Published In

Archiv der Mathematik

DOI

EISSN

1420-8938

ISSN

0003-889X

Publication Date

June 29, 2015

Volume

104

Issue

6

Start / End Page

561 / 575

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics