Geodesic
Einstein's equation on three-dimensional metric Lie groups with vector torsion
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 41-53

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

In this paper, we study the Einstein equation on three-dimensional Lie groups equipped with a left-invariant (pseudo) Riemannian metric and a metric connection with left-invariant vector torsion. We prove that all such Lie groups are either Einstein manifolds with respect to the Levi-Civita connection or conformally flat manifolds.
Keywords: Lie algebra, left-invariant (pseudo) Riemannian metric, Einstein manifold.
Mots-clés : Lie group, vector torsion 
@article{INTO_2020_181_a5,
     author = {P. N. Klepikov and E. D. Rodionov and O. P. Khromova},
     title = {Einstein's equation on three-dimensional metric {Lie} groups with vector torsion},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {41--53},
     publisher = {mathdoc},
     volume = {181},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_181_a5/}
}
TY  - JOUR
AU  - P. N. Klepikov
AU  - E. D. Rodionov
AU  - O. P. Khromova
TI  - Einstein's equation on three-dimensional metric Lie groups with vector torsion
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 41
EP  - 53
VL  - 181
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_181_a5/
LA  - ru
ID  - INTO_2020_181_a5
ER  - 
%0 Journal Article
%A P. N. Klepikov
%A E. D. Rodionov
%A O. P. Khromova
%T Einstein's equation on three-dimensional metric Lie groups with vector torsion
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 41-53
%V 181
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_181_a5/
%G ru
%F INTO_2020_181_a5
P. N. Klepikov; E. D. Rodionov; O. P. Khromova. Einstein's equation on three-dimensional metric Lie groups with vector torsion. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 41-53. http://geodesic.mathdoc.fr/item/INTO_2020_181_a5/