Comptes Rendus
no. 5
Differential geometry
A counterexample to Belgun–Moroianu conjecture

Presented by: Etienne Ghys

Vladimir S. Matveev1; Yuri Nikolayevsky2
1 Institute of Mathematics, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany
2 Department of Mathematics and Statistics, La Trobe University, Melbourne, 3086, VIC, Australia
Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 455-457.

We construct an example of a closed manifold with a nonflat reducible locally metric connection such that it preserves a conformal structure and such that it is not the Levi-Civita connection of a Riemannian metric.

Nous construisons un exemple de variété fermée munie d'une connexion réductible, qui n'est pas plate, qui transporte parallèlement une métrique riemannienne au voisinage de tout point, qui préserve une structure conforme et qui n'est pas la connexion de Levi-Civita d'une métrique riemannienne.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.03.001

Vladimir S. Matveev 1; Yuri Nikolayevsky 2

1 Institute of Mathematics, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany
2 Department of Mathematics and Statistics, La Trobe University, Melbourne, 3086, VIC, Australia 
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     title = {A counterexample to {Belgun{\textendash}Moroianu} conjecture},
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Vladimir S. Matveev; Yuri Nikolayevsky. A counterexample to Belgun–Moroianu conjecture. Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 455-457. doi : 10.1016/j.crma.2015.03.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.001/

[1] F. Belgun; A. Moroianu On the irreducibility of locally metric connections, J. Reine Angew. Math. (Crelle's Journal) (February 2014) | DOI

[2] C. Benson; C. Gordon Kähler structures on compact solvmanifolds, Proc. Amer. Math. Soc., Volume 108 (1990), pp. 971-980

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