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Framed curves in the Euclidean space

  • Shun’ichi Honda EMAIL logo und Masatomo Takahashi
Veröffentlicht/Copyright: 28. Juni 2016
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Advances in Geometry
Aus der Zeitschrift Advances in Geometry Band 16 Heft 3

Abstract

A framed curve in the Euclidean space is a curve with a moving frame. It is a generalization not only of regular curves with linear independent condition, but also of Legendre curves in the unit tangent bundle. We define smooth functions for a framed curve, called the curvature of the framed curve, similarly to the curvature of a regular curve and of a Legendre curve. Framed curves may have singularities. The curvature of the framed curve is quite useful to analyse the framed curves and their singularities. In fact, we give the existence and the uniqueness for the framed curves by using their curvature. As applications, we consider a contact between framed curves, and give a relationship between projections of framed space curves and Legendre curves.

Key words: Framed curve; existence; uniqueness; curvature of a framed curve; congruent as framed curves
MSC 2010: 58K05; 53A04; 53D35

Communicated by: K. Ono

References

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Received: 2014-3-26
Revised: 2014-10-17
Published Online: 2016-6-28
Published in Print: 2016-7-1

© 2016 by Walter de Gruyter Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Research Article
  3. Framed curves in the Euclidean space
  4. Research Article
  5. A characterization of the rate of change ofФ-entropy via an integral form curvature-dimension condition
  6. Research Article
  7. On the density function on moduli spaces of toric 4-manifolds
  8. Research Article
  9. Conformal Ricci solitons and related integrability conditions
  10. Research Article
  11. Inequalities for casorati curvatures of submanifolds in real space forms
  12. Research Article
  13. Inequalities for hyperconvex sets
  14. Research Article
  15. Neighborly inscribed polytopes and delaunay triangulations
  16. Research Article
  17. Cellular homology of real maximal isotropic grassmannians
  18. Research Article
  19. Symmetric subspaces of SE(3)
  20. Research Article
  21. Clifford’s Theorem for graphs
https://doi.org/10.1515/advgeom-2015-0035
Schlagwörter für diesen Artikel
Framed curve; existence; uniqueness; curvature of a framed curve; congruent as framed curves

Artikel in diesem Heft

  1. Frontmatter
  2. Research Article
  3. Framed curves in the Euclidean space
  4. Research Article
  5. A characterization of the rate of change ofФ-entropy via an integral form curvature-dimension condition
  6. Research Article
  7. On the density function on moduli spaces of toric 4-manifolds
  8. Research Article
  9. Conformal Ricci solitons and related integrability conditions
  10. Research Article
  11. Inequalities for casorati curvatures of submanifolds in real space forms
  12. Research Article
  13. Inequalities for hyperconvex sets
  14. Research Article
  15. Neighborly inscribed polytopes and delaunay triangulations
  16. Research Article
  17. Cellular homology of real maximal isotropic grassmannians
  18. Research Article
  19. Symmetric subspaces of SE(3)
  20. Research Article
  21. Clifford’s Theorem for graphs
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