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In a well-known paper, Stenzel constructed complete Ricci-flat Kahler metrics on the total spaces of cotangent bundles of $S^n$, $\mathbb{RP}^n,$ $\mathbb{CP}^n$, $\mathbb{HP}^n$, and $\mathbb{OP}^2$.

Is Stenzel's complete Ricci-flat Kahler metric on $T^*\mathbb{CP}^n$ hyperkahler?

Remark: Earlier, Calabi constructed a complete hyperkahler metric on $T^*\mathbb{CP}^n$. Dancer-Swann and Bielawski showed that Calabi's metrics are the unique complete irreducible hyperkahler metrics (of real dimension $\geq 8$) that are cohomogeneity-one under an action of a compact simple Lie group. Now, as Stenzel's metric is cohomogeneity-one (I think), if it's hyperkahler, then it must coincide with Calabi's metric.

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