Conformal Geodesics Cannot Spiral

Abstract

We show that conformal geodesics on a Riemannian manifold cannot spiral: there does not exist a conformal geodesic which becomes trapped in every neighbourhood of a point.

Wojciech Kamiński has provided a non real--analytic counterexample to Theorem 2.3. Apart from the missing assumption of real--analyticity the error is contained in Lemma 4.6 where it was claimed that the size of the heart is a continuous function. Other results the paper, in particular the definition of the exponential map, are unaffected by the above error.