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 http://dx.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.
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