Differential Geometry/Lie Algebras
Bach-flat Lie groups in dimension 4
Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 303-306.

We establish the existence of solvable Lie groups of dimension 4 and left-invariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.

Nous montrons lʼexistence de groupes de Lie résolubles de dimension 4 et de métriques riemanniennes invariantes à gauche, dont le tenseur de Bach est nul et qui ne sont ni conformément Einstein, ni semi-conformément plates.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.04.011
Abbena, Elsa 1; Garbiero, Sergio 1; Salamon, Simon 2

1 Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
2 Department of Mathematics, Kingʼs College London, Strand, London WC2L 2RS, UK
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Abbena, Elsa; Garbiero, Sergio; Salamon, Simon. Bach-flat Lie groups in dimension 4. Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 303-306. doi : 10.1016/j.crma.2013.04.011. http://www.numdam.org/articles/10.1016/j.crma.2013.04.011/

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