What question did this study set out to answer?

To prove the existence of a non-round Einstein metric invariant under a specific symmetry.

February 23, 2026

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.

Abstract

Abstract We prove the existence of a non‐round Einstein metric on that is invariant under the usual cohomogeneity one action of on . The proof involves using several rigorous numerical analysis techniques to produce a Riemannian metric which approximately satisfies the Einstein condition to known high precision, and then demonstrating that can be perturbed into a true Einstein metric .

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