Einstein–Maxwell Equations on Four-dimensional Lie Algebras
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 822-840

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

We classify up to automorphisms all left-invariant non-Einstein solutions to the Einstein–Maxwell equations on four-dimensional Lie algebras.
DOI : 10.4153/S0008439519000249
Mots-clés : Einstein–Maxwell metric, Lie algebra, Kähler metric, almost complex structure
Koca, Caner; Lejmi, Mehdi. Einstein–Maxwell Equations on Four-dimensional Lie Algebras. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 822-840. doi: 10.4153/S0008439519000249
@article{10_4153_S0008439519000249,
     author = {Koca, Caner and Lejmi, Mehdi},
     title = {Einstein{\textendash}Maxwell {Equations} on {Four-dimensional} {Lie} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {822--840},
     year = {2019},
     volume = {62},
     number = {4},
     doi = {10.4153/S0008439519000249},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000249/}
}
TY  - JOUR
AU  - Koca, Caner
AU  - Lejmi, Mehdi
TI  - Einstein–Maxwell Equations on Four-dimensional Lie Algebras
JO  - Canadian mathematical bulletin
PY  - 2019
SP  - 822
EP  - 840
VL  - 62
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000249/
DO  - 10.4153/S0008439519000249
ID  - 10_4153_S0008439519000249
ER  - 
%0 Journal Article
%A Koca, Caner
%A Lejmi, Mehdi
%T Einstein–Maxwell Equations on Four-dimensional Lie Algebras
%J Canadian mathematical bulletin
%D 2019
%P 822-840
%V 62
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000249/
%R 10.4153/S0008439519000249
%F 10_4153_S0008439519000249

[1] Apostolov, V., Calderbank, D. M. J., and Gauduchon, P., Ambitoric geometry I: Einstein metrics and extremal ambikähler structures . J. Reine Angew. Math. 721(2016), 109–147. Google Scholar | DOI

[2] Apostolov, V. and Maschler, G., Conformally Kähler, Einstein–Maxwell geometry . J. Eur. Math. Soc. 21(2019), no. 5, 1319–1360. Google Scholar | DOI

[3] Drăghici, T., On some 4-dimensional almost Kähler manifolds . Kodai Math. J. 18(1995), no. 1, 156–168. Google Scholar | DOI

[4] Fino, A., Almost Kähler 4-dimensional Lie groups with J-invariant Ricci tensor . Differential Geom. Appl. 23(2005), 1, 26–37. Google Scholar | DOI

[5] Futaki, A. and Ono, H., Conformally Einstein–Maxwell Kähler metrics and structure of the automorphism group . Math. Z. 292(2019), no. 1–2, 571–589. Google Scholar | DOI

[6] Futaki, A. and Ono, H., On the existence problem of Einstein–Maxwell Kähler metrics. arxiv:1803.06801 Google Scholar

[7] Futaki, A. and Ono, H., Volume minimization and conformally Kähler, Einstein–Maxwell geometry . J. Math. Soc. Japan 70(2018), 4, 1493–1521. Google Scholar | DOI

[8] Karki, M. B. and Thompson, G., Four-dimensional Einstein Lie groups . Differ. Geom. Dyn. Syst. 18(2016), 43–57. Google Scholar

[9] Koca, C. and Tønnesen-Friedman, C. W., Strongly Hermitian Einstein–Maxwell solutions on ruled surfaces . Ann. Global Anal. Geom. 50(2016), no. 1, 29–46. Google Scholar | DOI

[10] Lahdili, A., Conformally Kähler, Einstein–Maxwell metrics and boundedness of the modified Mabuchi-functional. arxiv:1710.00235 Google Scholar

[11] Lahdili, A., Automorphisms and deformations of conformally Kähler, Einstein–Maxwell metrics . J. Geom. Anal. 29(2019), no. 1, 542–568. Google Scholar | DOI

[12] Lebrun, C., The Einstein–Maxwell equations, extremal Kähler metrics, and Seiberg–Witten theory . In: The many facets of geometry . Oxford University Press, Oxford, 2010, pp. 17–33. Google Scholar | DOI

[13] Lebrun, C., The Einstein–Maxwell equations, Kähler metrics, and Hermitian geometry . J. Geom. Phys. 91(2015), 163–171. Google Scholar | DOI

[14] Lebrun, C., The Einstein–Maxwell equations and conformally Kähler geometry . Comm. Math. Phys. 344(2016), no. 2, 621–653. Google Scholar | DOI

[15] Mubarakzjanov, G. M., Classification of real structures of Lie algebras of fifth order . Izv. Vysš. Učebn. Zaved. Matematika 1963(1963), no. 3 (34), 99–106. Google Scholar

[16] Patera, J., Sharp, R. T., and Winternitz, P., Invariants of real low dimension Lie algebras . J. Math. Phys. 17(1976), 986–994. Google Scholar | DOI

[17] Shao, H., Compactness and rigidity of Kähler surfaces with constant scalar curvature. arxiv:1304.0853 Google Scholar

[18] Yamabe, H., On a deformation of Riemannian structures on compact manifolds . Osaka Math. J. 12(1960), 21–37. Google Scholar

Cité par Sources :