Holonomy algebras of Einstein pseudo-Riemannian manifolds

Abstract

The holonomy algebras of Einstein not Ricci-flat pseudo-Riemannian manifolds of arbitrary signature are classified. As illustrating examples, the cases of Lorentzian manifolds, pseudo-Riemannian manifolds of signature $(2,n)$ and the para-quaternionic-Kählerian manifolds with non-zero scalar curvature are considered. Einstein not Ricci-flat metrics of signature $(2,n)$ with all possible holonomy algebras are given.

final version accepted to Journal of the London Mathematical Society

References in corpus (4)

• Metrics that realize all Lorentzian holonomy algebras
• Ricci-Flat Holonomy: a Classification
• Holonomy of Einstein Lorentzian manifolds
• Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature

Cited by in corpus (1)

• Local Type III metrics with holonomy in ${\mathrm{G}}_2^{\ast }$