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 …

The set of osculating circles of a given curve in S 3 forms a lightlike curve in the set of
oriented circles in S 3. We show that its “1 2-dimensional measure” with respect to the …

By a conformal string in Euclidean space is meant a closed critical curve with non-constant
conformal curvatures of the conformal arclength functional. We prove that (1) the set of …

This article deals with the study of some properties of immersed curves in the conformal
sphere Q _n, viewed as a homogeneous space under the action of the Möbius group. After …

The set of osculating circles of a given curve in $\SS^ 3$ forms a curve in the set of oriented
circles in $\SS^ 3$. We show that its" ${\frac12} $-dimensional measure" with respect to the …

The conformal nature of smooth curves in $\mathbb {R}^ 3$ is characterised by conformal
length, curvature and torsion. We present a derivation of these conformal parameters via a …

1 Introduction Page 1 M obius invariants for pairs of spheres (Sm 1 ;Sl 2 ) in the M obius space
Sn Rolf Sulanke February 22, 1999 Abstract In this article we construct a complete system of M …

This paper studies the geometry of the critical points of the simplest conformally invariant
variational problem for timelike curves in the n-dimensional Einstein universe. Such critical …

Self-similar curves arise naturally as the tension-free equilibrium states of conformally
invariant bending energies. The simplest example is the M\" obius invariant conformal arc …

Any conformally invariant energy associated with a curve possesses tension-free
equilibrium states which are self-similar. When this energy is the three dimensional …