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 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.

On the Total CR Twist of Transversal Curves in the 3-Sphere

“…Remark 3.5. For the application of Griffiths' approach to other geometric variational problems, the reader is referred to [9,11,19,26,27,28,30]. 4 The CR twist of a critical curve…”