Holonomy algebras of Einstein pseudo-Riemannian manifolds
Differential Geometry
2021-05-14 v3
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 and the para-quaternionic-K\"ahlerian manifolds with non-zero scalar curvature are considered. Einstein not Ricci-flat metrics of signature with all possible holonomy algebras are given.
Keywords
Cite
@article{arxiv.1206.6623,
title = {Holonomy algebras of Einstein pseudo-Riemannian manifolds},
author = {Anton S. Galaev},
journal= {arXiv preprint arXiv:1206.6623},
year = {2021}
}
Comments
final version accepted to Journal of the London Mathematical Society