A hyperkähler metric on twisted cotangent bundles of the complex projective space

Abstract

We construct a hyperkähler metric on twisted cotangent bundles of the complex projective space ${\mathbb{CP}}^n$ explicitly in terms of local coordinates. Note that the twisted cotangent bundles of ${\mathbb{CP}}^n$ are holomorphically isomorphic to complex semisimple coadjoint orbits of ${\mathrm{SL}}_{n+1}(\mathbb{C})$.

19 pages