Computationally-assisted proof of a novel $\mathsf{O}(3)\times \mathsf{O}(10)$-invariant Einstein metric on $S^{12}$

Timothy Buttsworth, Liam Hodgkinson

We prove existence of a non-round Einstein metric $g$ on $S^{12}$ that is invariant under the usual cohomogeneity one action of $\mathsf{O}(3)\times \mathsf{O}(10)$ on $S^{12}\subse…