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

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

2010-03-21

arxiv.org/abs/1003.4014v2

Mathematics

Differential Geometry

16 pages

Scientific paper

The holonomy algebra of a pseudo-hyper-K\"ahlerian 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-K\"ahlerian symmetric spaces of index 4 is
obtained.

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