In mathematics, a Hartshorne ellipse is an ellipse in the unit ball bounded by the 4-sphere S4 such that the ellipse and the circle given by intersection of its plane with S4 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 S4.
- 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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