Conformal Geodesics Cannot Spiral -- Erratum
Peter Cameron, Maciej Dunajski, Paul Tod
TL;DR
This paper addresses a correction to a previous claim that conformal geodesics cannot spiral, providing a counterexample and analyzing the failure in the original proof.
Contribution
It presents a non real-analytic counterexample to the claim and clarifies the flaw in the original proof regarding conformal geodesics.
Findings
Counterexample shows conformal geodesics can spiral
Original proof of non-spiraling behavior is flawed
Clarifies conditions under which conformal geodesics may spiral
Abstract
Wojciech Kami\'nski has provided a non real-analytic counterexample to our claim in [1] that conformal geodesics cannot spiral. This erratum illustrates how the proof of Lemma 4.6 [1] (on which our claim was based) fails.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Holomorphic and Operator Theory · Mathematics and Applications