Joshua Lackman

Isometric Embeddings of Hyperk\"{a}hler $\mathrm{T}^*\mathbb{CP}^{n}$

We construct explicit $U(n)$-equivariant isometric embeddings $T^*\mathbb{CP}^{n-1} \hookrightarrow \mathbb{R}^{n^4+2n^2-1}$, $n\ge 2$, with respect to Calabi's hyperk\"{a}hler metric on $T^*\mathbb{CP}^{n-1}$. To achieve this, we first construct a diffeomorphism from $T^*\mathbb{CP}^{n-1}$ onto the manifold of rank-1...