Pseudo-Riemannian Lie groups admitting left-invariant conformal vector fields

Hui Zhang; Zhiqi Chen

doi:10.5802/crmath.23

Géométrie, Systèmes dynamiques

Pseudo-Riemannian Lie groups admitting left-invariant conformal vector fields
[Groupes de Lie pseudo-riemanniens admettant des champs vectoriels conformes invariants à gauche]

Hui Zhang ¹ ; Zhiqi Chen ²

¹ School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P.R. China
² Corresponding author. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P.R. China

Comptes Rendus. Mathématique, Volume 358 (2020) no. 2, pp. 143-149.

Résumé
Abstract

Soit $G$ un groupe de Lie lorentzien ou un groupe de Lie pseudo-riemannien de type $(n - 2, 2)$ . Si $G$ admet un champ vectoriel invariant à gauche non-Killing, alors $G$ est résoluble.

Let $G$ be a Lorentzian Lie group or a pseudo-Riemannian Lie group of type $(n - 2, 2)$ . If $G$ admits a non-Killing left-invariant conformal vector field, then $G$ is solvable.

Reçu le : 2019-12-26
Révisé le : 2020-02-21
Accepté le : 2020-02-21
Publié le : 2020-06-15

DOI : 10.5802/crmath.23

Classification : 53C25, 53C30, 22E60
Mots clés : Conformal vector fields, Killing vector fields, Pseudo-Riemannian Lie groups, Lorenztian Lie groups

Affiliations des auteurs :

Hui Zhang ¹ ; Zhiqi Chen ²

¹ School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P.R. China
² Corresponding author. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P.R. China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Hui Zhang and Zhiqi Chen},
     title = {Pseudo-Riemannian {Lie} groups admitting left-invariant conformal vector fields},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {143--149},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {2},
     year = {2020},
     doi = {10.5802/crmath.23},
     language = {en},
}

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Hui Zhang; Zhiqi Chen. Pseudo-Riemannian Lie groups admitting left-invariant conformal vector fields. Comptes Rendus. Mathématique, Volume 358 (2020) no. 2, pp. 143-149. doi : 10.5802/crmath.23. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.23/

Bibliographie
Cité par

[1] Dmitri Alekseevskii Self-similar Lorentzian manifolds, Ann. Global Anal. Geom., Volume 3 (1985) no. 1, pp. 59-84 | DOI | MR | Zbl

[2] Adriana Araujo; Zhiqi Chen; Benedito Leandro Conformal vector fields on Lie groups (2016) (https://arxiv.org/abs/1608.05943v2)

[3] Ezequiel Barbosa; Ernani jun. Ribeiro On conformal solutions of the Yamabe flow, Arch. Math., Volume 101 (2013) no. 1, pp. 79-89 | DOI | MR | Zbl

[4] Esteban Calviño-Louzao; Javier Seoane-Bascoy; María Elena Vázquez-Abal; Ramón Vázquez-Lorenzo Three-dimensional homogeneous Lorentzian Yamabe solitons, Abh. Math. Semin. Univ. Hamb., Volume 82 (2012) no. 2, pp. 193-203 | DOI | MR | Zbl

[5] Antonio Caminha The geometry of closed conformal vector fields on Riemannian spaces, Bull. Braz. Math. Soc. (N.S.), Volume 42 (2011) no. 2, pp. 277-300 | DOI | MR | Zbl

[6] Huai-Dong Cao; Xiaofeng Sun; Yingying Zhang On the structure of gradient Yamabe solitons, Math. Res. Lett., Volume 19 (2012) no. 4, pp. 767-774 | MR | Zbl

[7] Jacqueline Ferrand The action of conformal transformations on a Riemannian manifold, Math. Ann., Volume 304 (1996) no. 2, pp. 277-291 | DOI | MR | Zbl

[8] Charles Frances About pseudo-Riemannian Lichnerowicz conjecture, Transform. Groups, Volume 20 (2015) no. 4, pp. 1015-1022 | DOI | MR | Zbl

[9] Shu-Yu Hsu A note on compact gradient Yamabe solitons, J. Math. Anal. Appl., Volume 388 (2012) no. 2, pp. 725-726 | MR | Zbl

[10] Nathan Jacobson A note on automorphisms and derivations of Lie algebras, Proc. Am. Math. Soc., Volume 6 (1955), pp. 281-283 | DOI | MR | Zbl

[11] Wolfgang Kühnel; Hans-Bert Rademacher Essential conformal fields in pseudo-Riemannian geometry. II, J. Math. Sci., Tokyo, Volume 4 (1997) no. 3, pp. 649-662 | MR | Zbl

[12] M. Obata Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan, Volume 14 (1962), pp. 152-164 | DOI | MR | Zbl

[13] Barrett O’Neill Semi-Riemannian geometry with applications to relativity, Pure and Applied Mathematics, 103, Academic Press Inc., 1983 | MR | Zbl

[14] M.-N. Podoksënov Conformally homogeneous Lorentzian manifolds. II, Sib. Mat. Zh., Volume 33 (1992) no. 6, pp. 154-161 translation in Siberian Math. J. 33 (1992), p. 1087–1093 | MR | Zbl

[15] Ju Tan; Zhiqi Chen; Na Xu Conformal vector fields on Lorentzian Lie groups of dimension 4, J. Lie Theory, Volume 28 (2018) no. 3, pp. 761-769 | MR | Zbl

[16] Hermann Weyl Reine Infinitesimalgeometrie, Math. Z., Volume 26 (1918), pp. 384-411 | DOI | MR | Zbl

[17] Hui Zhang; Zhiqi Chen; S. Zhang Conformal vector fields on Lorentzian Lie groups of dimension 5 (2020) (to appear in J. Lie Theory)

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