Geodesics on a K3 Surface near the Orbifold Limit
Differential Geometry
2025-08-25 v1
Abstract
This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi-Yau metrics due to R. Kobayashi. As an application, we study stable closed geodesics. We use the metric estimates to show how there are generally restrictions on the existence of such geodesics. We also show how there can exist stable, closed geodesics in some highly symmetric circumstances due to hyperk\"{a}hler identities.
Cite
@article{arxiv.2209.04814,
title = {Geodesics on a K3 Surface near the Orbifold Limit},
author = {Jørgen Olsen Lye},
journal= {arXiv preprint arXiv:2209.04814},
year = {2025}
}
Comments
63 pages