Hartshorne ellipse

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.

References

• Hartshorne, Robin (1978), "Stable vector bundles and instantons", Communications in Mathematical Physics 59 (1): 1–15, doi:10.1007/BF01614151, ISSN 0010-3616, http://projecteuclid.org/euclid.cmp/1103901556