Papers › Computationally-assisted proof of a novel 𝖮(3)×𝖮(10)-invariant Einstein metric on S¹²
Computationally-assisted proof of a novel 𝖮(3)×𝖮(10)-invariant Einstein metric on S¹²
Timothy Buttsworth, Liam Hodgkinson
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We prove existence of a non-round Einstein metric g on S¹² that is invariant under the usual cohomogeneity one action of 𝖮(3)×𝖮(10) on S¹²⊂ℝ¹³= ℝ³⊕ℝ¹⁰. The proof involves using several rigorous numerical analysis techniques to produce a Riemannian metric ĝ which approximately satisfies the Einstein condition to known high precision, and then demonstrating that ĝ can be perturbed into a true Einstein metric g.
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