Homogeneous hyper-complex structures and the Joyceʼs construction

We prove that any invariant hyper-complex structure on a homogeneous space M = G / L where G is a compact Lie group is obtained via the Joyceʼs construction, provided that there exists a hyper-Hermitian naturally reductive invariant metric on M.

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Bibliographic Details
Published inDifferential geometry and its applications Vol. 29; no. 4; pp. 547 - 554
Main Authors Bedulli, Lucio, Gori, Anna, Podestà, Fabio
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2011
Subjects
Construction
Differential geometry
Homogeneous spaces
Hyper-complex structures
Hyper-Kähler with torsion
Invariants
Lie groups
53C30
Hyper-complex structures
Hyper-Kähler with torsion
53C26
Homogeneous spaces
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Summary:We prove that any invariant hyper-complex structure on a homogeneous space M = G / L where G is a compact Lie group is obtained via the Joyceʼs construction, provided that there exists a hyper-Hermitian naturally reductive invariant metric on M.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2011.04.033