Differential geometry
A counterexample to Belgun–Moroianu conjecture
[Un contre-exemple à la conjecture de Belgun–Moroianu]

Présenté par : Etienne Ghys

Matveev, Vladimir S.1 ; Nikolayevsky, Yuri2
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, Tome 353 (2015) no. 5, pp. 455-457.

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.

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.

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Accepté le :
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DOI : 10.1016/j.crma.2015.03.001
Matveev, Vladimir S. 1 ; Nikolayevsky, Yuri 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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Matveev, Vladimir S.; Nikolayevsky, Yuri. A counterexample to Belgun–Moroianu conjecture. Comptes Rendus. Mathématique, Tome 353 (2015) no. 5, pp. 455-457. doi : 10.1016/j.crma.2015.03.001. https://www.numdam.org/articles/10.1016/j.crma.2015.03.001/

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

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

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