Geodesic
The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case
Matematičeskie trudy, Tome 12 (2009) no. 1, pp. 40-116.

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain a complete classification of all the possible values of the signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional nonunimodular Lie groups. 
@article{MT_2009_12_1_a2,
     author = {A. G. Kremlyov and Yu. G. Nikonorov},
     title = {The signature of the {Ricci} curvature of left-invariant {Riemannian} metrics on four-dimensional {Lie} groups. {The} nonunimodular case},
     journal = {Matemati\v{c}eskie trudy},
     pages = {40--116},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2009_12_1_a2/}
}
TY  - JOUR
AU  - A. G. Kremlyov
AU  - Yu. G. Nikonorov
TI  - The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case
JO  - Matematičeskie trudy
PY  - 2009
SP  - 40
EP  - 116
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2009_12_1_a2/
LA  - ru
ID  - MT_2009_12_1_a2
ER  - 
%0 Journal Article
%A A. G. Kremlyov
%A Yu. G. Nikonorov
%T The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case
%J Matematičeskie trudy
%D 2009
%P 40-116
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2009_12_1_a2/
%G ru
%F MT_2009_12_1_a2
A. G. Kremlyov; Yu. G. Nikonorov. The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case. Matematičeskie trudy, Tome 12 (2009) no. 1, pp. 40-116. http://geodesic.mathdoc.fr/item/MT_2009_12_1_a2/

[1] Alekseevskii D. V., “Odnorodnye rimanovy prostranstva otritsatelnoi krivizny”, Matem. sb., 96(138):1 (1975), 93–117 | MR | Zbl

[2] Besse A. L., Mnogoobraziya Einshteina, Mir, M., 1990 | MR | Zbl

[3] Kremlev A. G., Nikonorov Yu. G., “Signatura krivizny Richchi levoinvariantnykh rimanovykh metrik na chetyrekhmernykh gruppakh Li. Unimodulyarnyi sluchai”, Mat. trudy, 11:2 (2008), 115–147

[4] Kurosh A. G., Kurs vysshei algebry, Nauka, M., 1968 | Zbl

[5] Mubarakzyanov G. M., “O razreshimykh algebrakh Li”, Izv. vuzov. Ser. matematika, 1963, no. 1(32), 114–123 | MR | Zbl

[6] Nikitenko E. V., Nikonorov Yu. G., “Shestimernye einshteinovy solvmnogoobraziya”, Mat. trudy, 8:1 (2005), 71–121 | MR

[7] Nikonorov Yu. G., “Ob einshteinovykh rasshireniyakh nilpotentnykh metricheskikh algebr Li”, Mat. trudy, 10:1 (2007), 164–190 | MR

[8] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR | Zbl

[9] Christodoulakis T., Papadopoulos G. O., Dimakis A., “Automorphisms of real four-dimensional Lie algebras and the invariant characterization of homogeneous 4-spaces”, J. Phys. A: Math. Gen., 36 (2003), 427–441 | DOI | MR | Zbl

[10] Jensen G., “The scalar curvature of left-invariant Riemannian metrics”, Indiana Univ. Math. J., 20 (1971), 1125–1143 | DOI | MR

[11] Ha Ku Yong, Lee Jong Bum, “Left-invariant metrics and curvatures on simply connected three-dimensional Lie groups”, Math. Nachr., 2008 (to appear)

[12] Kowalski O., Nikc̆ević S. Z̆., “On Ricci eigenvalues of locally homogeneous Riemannian 3-manifolds”, Geom. Dedicata, 62:1 (1996), 65–72 | DOI | MR | Zbl

[13] Milnor J., “Curvatures of left-invariant metrics on Lie groups”, Adv. Math., 21:3 (1976), 293–329 | DOI | MR | Zbl

[14] Patera J., Sharp R. T., Winternitz P., Zassenhaus H., “Invariants of real low dimension Lie algebras”, J. Mathematical Phys., 17:6 (1976), 986–994 | DOI | MR | Zbl

[15] Rainer M., Schmidt H.-J., “Inhomogeneous cosmological models with homogeneous inner hypersurface geometry”, Gen. Relativity Gravitation, 27:12 (1995), 1265–1293 | DOI | MR | Zbl