The geometry of canal surfaces and the length of curves in de Sitter space

Rémi Langevin; Gil Solanes

doi:https://doi.org/10.1515/ADVGEOM.2011.026

The geometry of canal surfaces and the length of curves in de Sitter space

Rémi Langevin, Gil Solanes

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

7 Citations (Scopus)

Abstract

We find the minimal value of the length in de Sitter space of closed space-like curves with non-vanishing non-space-like geodesic curvature vector. These curves are in correspondence with closed almost-regular canal surfaces, and their length is a natural magnitude in conformal geometry. As an application, we get a lower bound for the total conformal torsion of closed space curves. © de Gruyter 2011.

Original language	English
Pages (from-to)	585-601
Journal	Advances in Geometry
Volume	11
DOIs	https://doi.org/10.1515/ADVGEOM.2011.026
Publication status	Published - 1 Nov 2011

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abstract = "We find the minimal value of the length in de Sitter space of closed space-like curves with non-vanishing non-space-like geodesic curvature vector. These curves are in correspondence with closed almost-regular canal surfaces, and their length is a natural magnitude in conformal geometry. As an application, we get a lower bound for the total conformal torsion of closed space curves. {\textcopyright} de Gruyter 2011.",

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AB - We find the minimal value of the length in de Sitter space of closed space-like curves with non-vanishing non-space-like geodesic curvature vector. These curves are in correspondence with closed almost-regular canal surfaces, and their length is a natural magnitude in conformal geometry. As an application, we get a lower bound for the total conformal torsion of closed space curves. © de Gruyter 2011.

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