Naturally reductive pseudo-Riemannian Lie groups in low dimensions
Differential Geometry
2014-09-25 v1
Abstract
This work concerns the non-flat metrics on the Heisenberg Lie group of dimension three and the bi-invariant metrics on the solvable Lie groups of dimension four. On we prove that the property of the metric being naturally reductive is equivalent to the property of the center being non-degenerate. These metrics are Lorentzian algebraic Ricci solitons. We start with the indecomposable Lie groups of dimension four admitting bi-invariant metrics and which act on by isometries and we finally study some geometrical features on these spaces.
Keywords
Cite
@article{arxiv.1211.0884,
title = {Naturally reductive pseudo-Riemannian Lie groups in low dimensions},
author = {Viviana del Barco and Gabriela P. Ovando and Francisco Vittone},
journal= {arXiv preprint arXiv:1211.0884},
year = {2014}
}
Comments
Keywords: Pseudo-Riemannian spaces, naturally reductive, Lie groups, Heisenberg group