Citesc Despre Teorema Lui Lancret.pdf

S0002-9939-97-03692-7.pdf
Preview of Citesc despre teorema lui Lancret
🔗 Source: ams.org
📊 Size: 172 KB
📄 Pages: 7 pages
⬇️ Downloads: 152

Summary

The author presents a theorem of Lancret for general helices in a 3-dimensional real-space-form, which gives a relevant difference between hyperbolic and spherical geometries. The theorem states that a necessary and sufficient condition for a curve to be a general helix is that the ratio of curvature to torsion be constant. The author then studies two classical problems for general helices in the 3-sphere: solving natural equations and the closed curve problem. The results show that there are no nontrivial general helices in the hyperbolic case, while in the spherical case, general helices can be realized as geodesics in Hopf cylinders. Additionally, the author finds a rational one-parameter family of closed general helices living in the Hopf torus shaped on any immersed closed curve in the 2-sphere.

Description

The author presents a theorem of Lancret for general helices in a 3-dimensional real-space-form, which gives a relevant difference between hyperbolic and...

Technical Information

  • File Format: PDF
  • File Size: 172 KB
  • Pages: 7
  • Language: EN
  • Total Downloads: 152
  • Last Updated: 1 month ago

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