Computationally assisted proof of a novel O(3)×O(10)‐invariant Einstein metric on S12

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 .