A hyperk\"ahler metric on twisted cotangent bundles of the complex projective space

Takashi Hashimoto

A hyperk\"ahler metric on twisted cotangent bundles of the complex projective space

Differential Geometry 2025-12-25 v2 Symplectic Geometry

Authors: Takashi Hashimoto

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 $\mathrm{SL}_{n+1}(\mathbb{C})$ .

Keywords

hyperk"ahler metric cotangent bundle complex projective space coadjoint orbit

Cite

@article{arxiv.2507.06604,
  title  = {A hyperk\"ahler metric on twisted cotangent bundles of the complex projective space},
  author = {Takashi Hashimoto},
  journal= {arXiv preprint arXiv:2507.06604},
  year   = {2025}
}

Comments

19 pages

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