Geodesic
Homogeneous Riemannian manifolds with generic Ricci tensor
W/lodzimierz Jelonek1
1Institute of Mathematics Technical University of Cracow Warszawska 24 31-155 Krak/ow, Poland Institute of Mathematics Polish Academy of Sciences Cracow Branch /Sw. Tomasza 30 31-027 Krak/ow, Poland
Annales Polonici Mathematici, Volume 77 (2001) no. 3, pp. 271-287

See the original article notice from the Institute of Mathematics Polish Academy of Sciences source

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.
DOI: 10.4064/ap77-3-6
Keywords: describe homogeneous manifolds generic ricci tensor prove frak dimensional unimodular lie algebra dim frak frak every left invariant metric lie group lie algebra frak admits mutually opposite compatible left invariant almost hler structures

W/lodzimierz Jelonek  1

1 Institute of Mathematics Technical University of Cracow Warszawska 24 31-155 Krak/ow, Poland Institute of Mathematics Polish Academy of Sciences Cracow Branch /Sw. Tomasza 30 31-027 Krak/ow, Poland 
W/lodzimierz Jelonek. Homogeneous Riemannian manifolds
with generic Ricci tensor. Annales Polonici Mathematici, Volume 77 (2001) no. 3, pp. 271-287. doi: 10.4064/ap77-3-6
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