Homogeneous Riemannian manifolds with generic Ricci tensor
Volume 77 / 2001
Annales Polonici Mathematici 77 (2001), 271-287
MSC: 53C30, 53C15, 53D05.
DOI: 10.4064/ap77-3-6
Abstract
We describe homogeneous manifolds with generic Ricci tensor. We also prove that if ${\frak g}$ is a 4-dimensional unimodular Lie algebra such that dim$[{\frak g},{\frak g}]\le 2$ then every left-invariant metric on the Lie group $G$ with Lie algebra ${\frak g}$ admits two mutually opposite compatible left-invariant almost Kähler structures.
