title: Hartshorne ellipse
text: # 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 $S^4.$
  
  