6533b7dcfe1ef96bd127348d

RESEARCH PRODUCT

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

Gil SolanesRémi Langevin

subject

Mathematics - Differential GeometryDe Sitter spaceTorsion (algebra)Magnitude (mathematics)Conformal mapGeometryGeometry and TopologyClosed spaceConformal geometryUpper and lower boundsMathematicsGeodesic curvature

description

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.

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