Numerical Solutions of Kähler–Einstein Metrics on (Formula presented.) with Conical Singularities along a Smooth Quadric Curve

We solve for the $$SO(3)$$SO(3)-invariant Kähler–Einstein metric on (Formula presented.) with cone singularities along a smooth quadric curve using a numerical approach. The numerical results show the sharp range of angles (Formula presented.) for the solvability of equations, and the correct limit metric space (Formula presented.). These results exactly match our theoretical conclusion. We also point out the cause of incomplete classifications in Conti (Commun Math Phys 3:751–774, 2007).