Geodesic
Four-dimensional metric Lie groups with zero Schouten--Weyl tensor
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 271-330.

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

In this paper we investigate a left-invariant (pseudo)Riemannian metrics on four-dimensional Lie groups with zero Schouten–Weyl tensor. A complete classification of metric Lie algebras of such Lie groups is obtained.
Keywords: left-invariant (pseudo)Riemannian metrics, Lie groups, Ricci operator, Segre types.
Mots-clés : Schouten–Weyl tensor 
@article{SEMR_2019_16_a50,
     author = {P. N. Klepikov},
     title = {Four-dimensional metric {Lie} groups with zero {Schouten--Weyl} tensor},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {271--330},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a50/}
}
TY  - JOUR
AU  - P. N. Klepikov
TI  - Four-dimensional metric Lie groups with zero Schouten--Weyl tensor
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 271
EP  - 330
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a50/
LA  - ru
ID  - SEMR_2019_16_a50
ER  - 
%0 Journal Article
%A P. N. Klepikov
%T Four-dimensional metric Lie groups with zero Schouten--Weyl tensor
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 271-330
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a50/
%G ru
%F SEMR_2019_16_a50
P. N. Klepikov. Four-dimensional metric Lie groups with zero Schouten--Weyl tensor. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 271-330. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a50/

[1] A. Besse, Einstein manifolds, Springer-Verlag, Berlin–Heidelberg, 1987 | MR | Zbl

[2] A. Gray, “Einstein-like manifolds whish are not Einstein”, Geom. Dedicata, 7 (1978), 259–280 | DOI | MR | Zbl

[3] O.P. Gladunova, E.D. Rodionov, V.V. Slavskii, “Harmonic Tensors on Three-Dimensional Lie Groups with Left-Invariant Lorentz Metric”, Journal of mathematical sciences, 198:5 (2014), 505–545 | DOI | MR

[4] O.P. Gladunova, V.V. Slavskii, “Left-invariant Riemannian metrics on four-dimensional unimodular Lie groups with zero-divergence Weyl tensor”, Doklady Mathematics, 81:2 (2010), 298–300 | DOI | MR | Zbl

[5] D.S. Voronov, E.D. Rodionov, “Left-invariant Riemannian metrics on four-dimensional nonunimodular Lie groups with zero-divergence Weyl tensor”, Doklady Mathematics, 81:3 (2010), 392–394 | DOI | MR | Zbl

[6] O.P. Gladunova, V.V. Slavskii, “Harmonicity of the Weyl tensor of left-invariant Riemannian metrics on four-dimensional unimodular Lie groups”, Siberian Advances in math., 23:1 (2013), 32–46 | DOI | MR

[7] A. Zaeim, A. Haji-Badali, “Einstein-like Pseudo-Riemannian Homogeneous Manifolds of Dimension Four”, Mediterranean Journal of Mathematics, 13:5 (2016), 3455–3468 | DOI | MR | Zbl

[8] G. Calvaruso, A. Zaeim, “Conformally flat homogeneous pseudo-riemannian four-manifolds”, Tohoku Math. J., 66 (2014), 31–54 | DOI | MR | Zbl

[9] G. Calvaruso, A. Zaeim, “Four-dimensional Lorentzian Lie groups”, Differential Geometry and its Applications, 31 (2013), 496–509 | DOI | MR | Zbl

[10] G. Calvaruso, A. Zaeim, “Neutral Metrics on Four-Dimensional Lie Groups”, Journal of Lie Theory, 25 (2015), 1023–1044 | MR | Zbl

[11] P.R. Law, Algebraic classification of the Ricci curvature tensor and spinor for neutral signature in four dimensions, 2010, arXiv: 1008.0444

[12] B. O'Neill, Semi-Riemannian Geometry With Applications to Relativity, Academic Press, 1983 | MR | Zbl

[13] O.P. Khromova, P.N. Klepikov, E.D. Rodionov, Left-invariant pseudo-Riemannian metrics on four-dimensional Lie groups with zero Schouten-Weyl tensor, 2016, arXiv: 1611.00916 | MR