# Hartshorne ellipse

In mathematics, a **Hartshorne ellipse** is an ellipse in the unit ball bounded by the 4-sphere **S**^{4} such that the ellipse and the circle given by intersection of its plane with **S**^{4} satisfy the Poncelet condition that there is a triangle with vertices on the circle and edges tangent to the ellipse. They were introduced by Hartshorne (1978), who showed that they correspond to *k* = 2 instantons on **S**^{4}.

## References

- Hartshorne, Robin (1978), "Stable vector bundles and instantons",
*Communications in Mathematical Physics*,**59**(1): 1–15, doi:10.1007/BF01614151, ISSN 0010-3616, MR 0480510

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