Holonomy algebras of pseudo-hyper-Kählerian manifolds of index 4

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Authors	BEZVITNAYA Natalia
Year of publication	2013
Type	Article in Periodical
Magazine / Source	Differential Geometry and its Applications
MU Faculty or unit	Faculty of Science
Citation
Doi	https://doi.org/10.1016/j.difgeo.2012.11.001
Field	General mathematics
Keywords	Pseudo-hyper-Kählerian manifold; Holonomy algebra; Curvature tensor; Symmetric space
Description	The holonomy algebra of a pseudo-hyper-Kählerian manifold of signature (4,4n+4) is a subalgebra of sp(1,n+1). Possible holonomy algebras of these manifolds are classified. Using this, a new proof of the classification of simply connected pseudo-hyper-Kählerian symmetric spaces of index 4 is obtained.
Related projects:	Algebraic and geometric methods and structures Algebraické metody v geometrii s potenciálem k aplikacím