Geodesics on a K3 Surface near the Orbifold Limit

DOI10.1007/S10455-023-09898-WarXiv2209.04814WikidataQ123244358 ScholiaQ123244358MaRDI QIDQ6410324

Publication date: 11 September 2022

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.

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Calabi-Yau theory (complex-analytic aspects) (32Q25) Geodesics in global differential geometry (53C22)

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