Invariant hyperkahler structures on the cotangent bundles of Hermitian symmetric spaces

Details Invariant hyperkahler structures on the cotangent bundles of Hermitian symmetric spaces Invariant hyperkahler structures on the cotangent bundles of Hermitian symmetric spaces

2003-02-17

arxiv.org/abs/math/0302187v2

Mathematics

Differential Geometry

24 pages, AMSTEX,some offprints and the proof of Lemma 4.10 are corrected

Scientific paper

Let $G/K$ be an irreducible Hermitian symmetric spaces of compact type with the standard homogeneous complex structure. Then the real symplectic manifold $(T^*(G/K),\Omega)$ has the natural complex structure $J^-$. We construct all $G$-invariant K\"ahler structures $(J,\Omega)$ on homogeneous domains in $T^*(G/K)$ anticommuting with $J^-$. Each such a hypercomplex structure, together with a suitable metric, defines a hyperk\"ahler structure. As an application, we obtain a new proof of the Harish-Chandra and Moore theorem.

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