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The geometry of canal surfaces and the length of curves in de Sitter space
-
Rémi Langevin
and
Gil Solanes
Published/Copyright:
November 11, 2011
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.
Received: 2009-06-15
Revised: 2009-09-17
Published Online: 2011-11-11
Published in Print: 2011-November
© de Gruyter 2011
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Articles in the same Issue
- Quasigeodesics and farthest points on convex surfaces
- The geometry of canal surfaces and the length of curves in de Sitter space
- On the mutual position of two irreducible conics in PG(2, q), q odd
- On the symmetric average of a convex body
- Ample vector bundles and polarized manifolds of sectional genus three
- Flat Laguerre planes of Kleinewillinghöfer type III.B
- Quotients of hypersurfaces in weighted projective space
- Characterizing the mixed volume
- Uniqueness of lattice packings and coverings of extreme density
- On the classification of convex lattice polytopes
- Blichfeldt-type inequalities and central symmetry
- Valuations on function spaces
