We prove that any invariant hypercomplex structure on a homogeneous space $M = G/L$ where $G$ is a compact Lie group is obtained via the Joyce's construction, provided that there exists a hyper-Hermitian naturally reductive invariant metric on $M$.
Homogeneous hypercomplex structures and the Joyce's construction / L. Bedulli, A. Gori, F. Podestà. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - 29:4(2011 Aug), pp. 547-554.
Homogeneous hypercomplex structures and the Joyce's construction
A. GoriSecondo
;
2011
Abstract
We prove that any invariant hypercomplex structure on a homogeneous space $M = G/L$ where $G$ is a compact Lie group is obtained via the Joyce's construction, provided that there exists a hyper-Hermitian naturally reductive invariant metric on $M$.
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