Geodesics on a K3 surface near the orbifold limit

Jørgen Olsen Lye

doi:10.48550/arXiv.2209.04814

Details

Original language	English
Article number	20
Journal	Annals of Global Analysis and Geometry
Volume	63
Issue number	3
Early online date	3 Apr 2023
Publication status	Published - Apr 2023

Abstract

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.

Keywords

Calabi–Yau, Closed geodesics, Complex Monge–Ampère, Hyperkähler

ASJC Scopus subject areas

Mathematics(all)
Analysis
Mathematics(all)
Geometry and Topology

Cite this

Geodesics on a K3 surface near the orbifold limit. / Lye, Jørgen Olsen.
In: Annals of Global Analysis and Geometry, Vol. 63, No. 3, 20, 04.2023.

Research output: Contribution to journal › Article › Research › peer review

Lye, JO 2023, 'Geodesics on a K3 surface near the orbifold limit', Annals of Global Analysis and Geometry, vol. 63, no. 3, 20. https://doi.org/10.48550/arXiv.2209.04814, https://doi.org/10.1007/s10455-023-09898-w

Lye, J. O. (2023). Geodesics on a K3 surface near the orbifold limit. Annals of Global Analysis and Geometry, 63(3), Article 20. https://doi.org/10.48550/arXiv.2209.04814, https://doi.org/10.1007/s10455-023-09898-w

Lye JO. Geodesics on a K3 surface near the orbifold limit. Annals of Global Analysis and Geometry. 2023 Apr;63(3):20. Epub 2023 Apr 3. doi: 10.48550/arXiv.2209.04814, 10.1007/s10455-023-09898-w

Lye, Jørgen Olsen. / Geodesics on a K3 surface near the orbifold limit. In: Annals of Global Analysis and Geometry. 2023 ; Vol. 63, No. 3.

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