Holonomy algebras of pseudo-quaternionic-Kählerian manifolds of signature $(4,4)$

Abstract

Possible holonomy algebras of pseudo-quaternionic-Kählerian manifolds of signature $(4,4)$ are classified. Using this, a new proof of the classification of simply connected pseudo-quaternionic-Kählerian symmetric spaces of signature $(4,4)$ is obtained.

16 pages

References in corpus (4)

• Metrics that realize all Lorentzian holonomy algebras
• Holonomy groups and special geometric structures of pseudo-Kählerian manifolds of index 2
• The classification problem for pseudo-Riemannian symmetric spaces
• Weakly irreducible subgroups of $Sp(1,n+1)$

Cited by in corpus (1)

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