On <i>m</i>-th root metrics with special curvature properties

Akbar Tayebi; Behzad Najafi

doi:10.1016/j.crma.2011.06.004

Differential Geometry

On m-th root metrics with special curvature properties
[Sur les métriques racines m-ièmes ayant des propriétés de courbure spéciales]

Présenté par : the Editorial Board

Akbar Tayebi ¹ ; Behzad Najafi ²

¹ Department of Mathematics, Qom University, Qom, Iran
² Department of Mathematics, Shahed University, Tehran, Iran

Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 691-693.

Résumé
Abstract

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 : 2011-04-13
Accepté le : 2011-06-06
Publié le : 2011-06-01

DOI : 10.1016/j.crma.2011.06.004

Affiliations des auteurs :

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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     author = {Akbar Tayebi and Behzad Najafi},
     title = {On \protect\emph{m}-th root metrics with special curvature properties},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {691--693},
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     volume = {349},
     number = {11-12},
     year = {2011},
     doi = {10.1016/j.crma.2011.06.004},
     language = {en},
}

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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/

Bibliographie
Cité par

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[2] V. Balan Numerical multilinear algebra of symmetric m-root structures. Spectral properties and applications, Symmetry Festival 2009, Budapest, Hungary (Symmetry: Culture and Science), Volume 21 (2010) no. 1–3, pp. 119-131

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[7] B. Najafi; Z. Shen; A. Tayebi Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geom. Dedicata, Volume 131 (2008), pp. 87-97

[8] A. Tayebi; B. Najafi On m-th root Finsler metrics, J. Geom. Phys., Volume 61 (2011) no. 8, pp. 1479-1484

[9] Y. Yu; Y. You On Einstein m-th root metrics, Differential Geometry and its Applications, Volume 28 (2010), pp. 290-294

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