TY - JOUR

T1 - Geodesics on a K3 surface near the orbifold limit

AU - Lye, Jørgen Olsen

N1 - Funding Information: This work is both a summary and continuation of the authors’ PhD thesis [51] written at the Albert-Ludwigs-Universität Freiburg under the expert guidance of Nadine Große and Katrin Wendland. The project was suggested by them, and several ideas and suggestions (and the absence of several mistakes) are due to them. They both took the time to read several earlier drafts of this paper in detail and provided helpful feedback. Any remaining errors are solely the author’s fault. We would also like to thank the anonymous referee for encouraging words and good suggestions for improvement.

PY - 2023/4

Y1 - 2023/4

N2 - This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi–Yau metrics due to 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 hyperkähler identities.

AB - This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi–Yau metrics due to 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 hyperkähler identities.

KW - Calabi–Yau

KW - Closed geodesics

KW - Complex Monge–Ampère

KW - Hyperkähler

UR - http://www.scopus.com/inward/record.url?scp=85152561439&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2209.04814

DO - 10.48550/arXiv.2209.04814

M3 - Article

AN - SCOPUS:85152561439

VL - 63

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

SN - 0232-704X

IS - 3

M1 - 20

ER -