English

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 (2,n)(2,n) and the para-quaternionic-K\"ahlerian manifolds with non-zero scalar curvature are considered. Einstein not Ricci-flat metrics of signature (2,n)(2,n) 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