Conformal geometry of timelike curves in the (1+2)-Einstein universe

Abstract

We study the conformal geometry of timelike curves in the (1+2)-Einstein universe, the conformal compactification of Minkowski 3-space defined as the quotient of the null cone of ${\mathbb{R}}^{2,3}$ by the action by positive scalar multiplications. The purpose is to describe local and global conformal invariants of timelike curves and to address the question of existence and properties of closed trajectories for the conformal strain functional. Some relations between the conformal geometry of timelike curves and the geometry of knots and links in the 3-sphere are discussed.

31 pages, 13 figures

References in corpus (2)

• Closed trajectories of a particle model on null curves in anti-de Sitter 3-space
• Quantization of the conformal arclength functional on space curves

Cited by in corpus (6)

• On the restricted conformal group of the (1+n)-Einstein static universe
• Critical Robertson-Walker universes
• Topologically embedded pseudospherical cylinders
• Conformal geometry of quasi-umbilical timelike surfaces
• On the Total CR Twist of Transversal Curves in the 3-Sphere
• On the Cauchy-Riemann geometry of transversal curves in the 3-sphere