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A hyperkähler metric on twisted cotangent bundles of the complex projective space
Published 9 Jul 2025 in math.DG and math.SG | (2507.06604v1)
Abstract: We construct a hyperk\"ahler 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 $\mathrm{SL}_{n+1}(\mathbb{C})$.
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