Abstract:
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.
Fulltext:
PDF file (457 kB)
