Hyper-Kähler instantons, symmetries, and flat spaces

Araneda, Bernardo

doi:10.1142/S0129055X24500338

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Hyper-Kähler instantons, symmetries, and flat spaces

MPS-Authors

/persons/resource/persons262649

Araneda, Bernardo
Geometry and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

2312.16136.pdf
(Preprint), 273KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Araneda, B. (2024). Hyper-Kähler instantons, symmetries, and flat spaces. Reviews in Mathematical Physics. doi:10.1142/S0129055X24500338.

Cite as: https://hdl.handle.net/21.11116/0000-0010-3A07-6

Abstract

We find all hyper-K\"ahler 4-manifolds admitting conformal K\"ahler
structures with respect to either orientation, and we show that these
structures can be expressed as a combination of twistor elementary states (and
possibly a self-dual dyon) in locally flat spaces. The complex structures of
different flat pieces are not compatible however, reflecting that the global
geometry is not a linear superposition. For either orientation the space must
be Gibbons-Hawking (thus excluding the Atiyah-Hitchin metric), and, if the
orientations are opposite, it must also be toric and have an irreducible
Killing tensor. We also show that the only hyper-K\"ahler 4-metric with a
non-constant Killing-Yano tensor is the half-flat Taub-NUT instanton.