Geodesics on a K3 Surface near the Orbifold Limit

2022/09/11 by Jørgen Olsen Lye, Lye, Jørgen Olsen
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #53C21 #53C22 #53C26 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geophysics and Gravity Measurements

paper · pdf · doi:10.48550/arxiv.2209.04814

openalex publication_date 2022/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 hyperkähler identities.

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