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

2011/08/11 by Langevin, Rémi, Solanes, Gil
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1108.2363

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.

Related

• Ordering curves on surfaces
• The minima of the geodesic length functions of uniform filling curves
• Lengths of simple loops on surfaces with hyperbolic metrics
• On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents
• Length spectral rigidity of non-positively curved surfaces