Comptes Rendus
Differential Geometry
On m-th root metrics with special curvature properties
[Sur les métriques racines m-ièmes ayant des propriétés de courbure spéciales]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 691-693.

Dans cette Note, nous montrons que toutes les métriques de Finsler racines m-ièmes ayant une courbure de Landsberg isotrope se réduisent à une métrique de Landsberg. Nous montrons ensuite que toutes les métriques de Finsler racines m-ièmes ayant une H-courbure presque nulle ont en fait une H-courbure nulle.

In this Note, we prove that every m-th root Finsler metric with isotropic Landsberg curvature reduces to a Landsberg metric. Then, we show that every m-th root metric with almost vanishing H-curvature has vanishing H-curvature.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.06.004

Akbar Tayebi 1 ; Behzad Najafi 2

1 Department of Mathematics, Qom University, Qom, Iran
2 Department of Mathematics, Shahed University, Tehran, Iran
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Akbar Tayebi; Behzad Najafi. On m-th root metrics with special curvature properties. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 691-693. doi : 10.1016/j.crma.2011.06.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.004/

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