This proof finds a non-round Einstein metric on S12 using numerical analysis techniques, implying new geometric insights.
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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Buttsworth et al. (2026) studied this question.
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