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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@article{CRMATH_2015__353_5_455_0, author = {Matveev, Vladimir S. and Nikolayevsky, Yuri}, title = {A counterexample to {Belgun{\textendash}Moroianu} conjecture}, journal = {Comptes Rendus. Math\'ematique}, pages = {455--457}, publisher = {Elsevier}, volume = {353}, number = {5}, year = {2015}, doi = {10.1016/j.crma.2015.03.001}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.crma.2015.03.001/} }
TY - JOUR AU - Matveev, Vladimir S. AU - Nikolayevsky, Yuri TI - A counterexample to Belgun–Moroianu conjecture JO - Comptes Rendus. Mathématique PY - 2015 SP - 455 EP - 457 VL - 353 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2015.03.001/ DO - 10.1016/j.crma.2015.03.001 LA - en ID - CRMATH_2015__353_5_455_0 ER -
%0 Journal Article %A Matveev, Vladimir S. %A Nikolayevsky, Yuri %T A counterexample to Belgun–Moroianu conjecture %J Comptes Rendus. Mathématique %D 2015 %P 455-457 %V 353 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2015.03.001/ %R 10.1016/j.crma.2015.03.001 %G en %F CRMATH_2015__353_5_455_0
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/
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