# Spiraling conformal geodesics

## TL;DR

This paper constructs a non-analytic example of a spiraling conformal geodesic in three-dimensional Euclidean space, addressing an open question and suggesting possible extensions to real analytic metrics in higher dimensions.

## Contribution

It provides the first explicit example of a non-analytic spiraling conformal geodesic in 3D Euclidean space, answering an open question in the field.

## Key findings

- Existence of non-analytic spiraling conformal geodesics in 3D Euclidean space.
- Potential to extend constructions to real analytic metrics in higher dimensions.
- Addresses an open question posed by Friedrich and Tod.

## Abstract

In this short note, we construct an example of spiraling conformal geodesic in Euclidean signature in dimension $3$, answering the question posed by Helmuth Friedrich and Paul Tod, if such objects exists. Our example is not real analytic, but similar constructions can lead also to real analytic metrics in arbitrary dimensions.