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

Author

Gil Solanes and Rémi Langevin

Subjects
Mathematics - Differential Geometry, De Sitter space, Torsion (algebra), Magnitude (mathematics), Conformal map, Geometry, Geometry and Topology, Closed space, Conformal geometry, Upper and lower bounds, Mathematics, Geodesic curvature
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.

Published
2011

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