Holonomy algebras of pseudo-hyper-K\"ahlerian manifolds of index 4

Natalia I. Bezvitnaya

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arXiv · 1003.4014

Holonomy algebras of pseudo-hyper-K\"ahlerian manifolds of index 4

Natalia I. Bezvitnaya

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Abstract

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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Natalia I. Bezvitnaya. 2010-03-21. Holonomy algebras of pseudo-hyper-K\"ahlerian manifolds of index 4. https://arxiv.org/abs/1003.4014

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