Geodesic
Classification of generalized Einstein metrics on three-dimensional Lie groups
Canadian journal of mathematics, Tome 75 (2023) no. 6, pp. 2038-2095

Voir la notice de l'article provenant de la source Cambridge

DOI

We develop the theory of left-invariant generalized pseudo-Riemannian metrics on Lie groups. Such a metric accompanied by a choice of left-invariant divergence operator gives rise to a Ricci curvature tensor, and we study the corresponding Einstein equation. We compute the Ricci tensor in terms of the tensors (on the sum of the Lie algebra and its dual) encoding the Courant algebroid structure, the generalized metric, and the divergence operator. The resulting expression is polynomial and homogeneous of degree 2 in the coefficients of the Dorfman bracket and the divergence operator with respect to a left-invariant orthonormal basis for the generalized metric. We determine all generalized Einstein metrics on three-dimensional Lie groups.
DOI : 10.4153/S0008414X23000056
Mots-clés : generalized Einstein metrics, left-invariant solutions on Lie groups, Ricci solitons 
Cortés, Vicente; Krusche, David. Classification of generalized Einstein metrics on three-dimensional Lie groups. Canadian journal of mathematics, Tome 75 (2023) no. 6, pp. 2038-2095. doi: 10.4153/S0008414X23000056
@article{10_4153_S0008414X23000056,
     author = {Cort\'es, Vicente and Krusche, David},
     title = {Classification of generalized {Einstein} metrics on three-dimensional {Lie} groups},
     journal = {Canadian journal of mathematics},
     pages = {2038--2095},
     year = {2023},
     volume = {75},
     number = {6},
     doi = {10.4153/S0008414X23000056},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000056/}
}
TY  - JOUR
AU  - Cortés, Vicente
AU  - Krusche, David
TI  - Classification of generalized Einstein metrics on three-dimensional Lie groups
JO  - Canadian journal of mathematics
PY  - 2023
SP  - 2038
EP  - 2095
VL  - 75
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000056/
DO  - 10.4153/S0008414X23000056
ID  - 10_4153_S0008414X23000056
ER  - 
%0 Journal Article
%A Cortés, Vicente
%A Krusche, David
%T Classification of generalized Einstein metrics on three-dimensional Lie groups
%J Canadian journal of mathematics
%D 2023
%P 2038-2095
%V 75
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000056/
%R 10.4153/S0008414X23000056
%F 10_4153_S0008414X23000056

Cité par Sources :