Geodesic
Einstein equation on three-dimensional locally homogeneous (pseudo)Riemannian manifolds with vectorial torsion
Matematičeskie zametki SVFU, Tome 28 (2021), pp. 30-47.

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

A metric connection with vectorial torsion, or a semi-symmetric metric connection, was discovered by E. Cartan. Later, many mathematicians studied the properties of this connection. For example, K. Yano, I. Agricola and other mathematicians investigated the properties of the curvature tensor, geodesic lines, and also the behavior of the connection under conformal deformations of the original metric. In this paper, we study the Einstein equation on three-dimensional locally homogeneous (pseudo)Riemannian manifolds with metric connection with invariant vectorial torsion. A theorem is obtained stating that all such manifolds are either Einstein manifolds with respect to the Levi-Civita connection or conformally flat. Earlier, the Einstein equation in the case of three-dimensional locally symmetric (pseudo)Riemannian manifolds have been investigated by the authors.
Keywords: Einstein manifold, invariant (pseudo)Riemannian metric, Lie algebra, locally homogeneous space
Mots-clés : vectorial torsion. 
@article{SVFU_2021_28_a2,
     author = {P. N. Klepikov and E. D. Rodionov and O. P. Khromova},
     title = {Einstein equation on three-dimensional locally homogeneous {(pseudo)Riemannian} manifolds with vectorial torsion},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {30--47},
     publisher = {mathdoc},
     volume = {28},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2021_28_a2/}
}
TY  - JOUR
AU  - P. N. Klepikov
AU  - E. D. Rodionov
AU  - O. P. Khromova
TI  - Einstein equation on three-dimensional locally homogeneous (pseudo)Riemannian manifolds with vectorial torsion
JO  - Matematičeskie zametki SVFU
PY  - 2021
SP  - 30
EP  - 47
VL  - 28
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVFU_2021_28_a2/
LA  - ru
ID  - SVFU_2021_28_a2
ER  - 
%0 Journal Article
%A P. N. Klepikov
%A E. D. Rodionov
%A O. P. Khromova
%T Einstein equation on three-dimensional locally homogeneous (pseudo)Riemannian manifolds with vectorial torsion
%J Matematičeskie zametki SVFU
%D 2021
%P 30-47
%V 28
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVFU_2021_28_a2/
%G ru
%F SVFU_2021_28_a2
P. N. Klepikov; E. D. Rodionov; O. P. Khromova. Einstein equation on three-dimensional locally homogeneous (pseudo)Riemannian manifolds with vectorial torsion. Matematičeskie zametki SVFU, Tome 28 (2021), pp. 30-47. http://geodesic.mathdoc.fr/item/SVFU_2021_28_a2/