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

2025/07/09 by Takashi Hashimoto, Hashimoto, Takashi
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2507.06604

openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a hyperkähler metric on twisted cotangent bundles of the complex projective space \mathbbCPⁿ explicitly in terms of local coordinates. Note that the twisted cotangent bundles of \mathbbCPⁿ are holomorphically isomorphic to complex semisimple coadjoint orbits of SL_n+1(ℂ).

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• Hyperkahler metrics near Lagrangian submanifolds and symplectic groupoids
• Deformations of hyperkähler cones
• Twisted cotangent bundles of Hyperkähler manifolds
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