Computationally assisted proof of a novel O (3) ×O (10) O (3) O (10) ‐invariant Einstein metric on S12S^12

Key Points

• To prove the existence of a non-round Einstein metric invariant under a specific symmetry.
• Rigorous numerical analysis techniques were employed.
• Construction of an approximate Riemannian metric satisfying the Einstein condition.
• Demonstration of perturbation into a true Einstein metric.
• Demonstrated the existence of a non-round Einstein metric on S12.
• Achieved high precision in satisfying the Einstein condition.