Geodesic
Invariant hyperk\"ahler structures on the~cotangent bundles of
Sbornik. Mathematics, Tome 194 (2003) no. 8, pp. 1225-1250

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Let $G/K$ be an irreducible Hermitian symmetric space of compact type with standard homogeneous complex structure. Then the real symplectic manifold $(T^*(G/K),\Omega)$ has the natural complex structure $J^-$. All $G$-invariant Kéhler structures $(J,\Omega)$ on $G$-invariant subdomains of $T^*(G/K)$ anticommuting with $J^-$ are constructed. Each hypercomplex structure of this kind, equipped with a suitable metric, defines a hyperkéhler structure. As an application, a new proof of the theorem of Harish-Chandra and Moore for Hermitian symmetric spaces is obtained. 
@article{SM_2003_194_8_a5,
     author = {I. V. Mykytyuk},
     title = {Invariant hyperk\"ahler structures on the~cotangent bundles of},
     journal = {Sbornik. Mathematics},
     pages = {1225--1250},
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     volume = {194},
     number = {8},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_8_a5/}
}
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I. V. Mykytyuk. Invariant hyperk\"ahler structures on the~cotangent bundles of. Sbornik. Mathematics, Tome 194 (2003) no. 8, pp. 1225-1250. http://geodesic.mathdoc.fr/item/SM_2003_194_8_a5/