no. 11-12
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

Tayebi, Akbar1 ; Najafi, Behzad2
1 Department of Mathematics, Qom University, Qom, Iran
2 Department of Mathematics, Shahed University, Tehran, Iran
Comptes Rendus. Mathématique, Tome 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
Tayebi, Akbar 1 ; Najafi, Behzad 2

1 Department of Mathematics, Qom University, Qom, Iran
2 Department of Mathematics, Shahed University, Tehran, Iran 
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Tayebi, Akbar; Najafi, Behzad. On m-th root metrics with special curvature properties. Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 691-693. doi : 10.1016/j.crma.2011.06.004. http://www.numdam.org/articles/10.1016/j.crma.2011.06.004/

[1] Akbar-Zadeh, H. Sur les espaces de Finsler á courbures sectionnelles constantes, Bull. Acad. Roy. Belg. Cl. Sci. (5), Volume LXXXIV (1988), pp. 281-322

[2] Balan, V. 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

[3] Balan, V. CMC and minimal surfaces in Berwald–Moor spaces, Hypercomplex Numbers in Geometry and Physics, Volume 3 (2006) no. 2(6), pp. 113-122

[4] Balan, V.; Perminov, N. Applications of resultants in the spectral m-root framework, Applied Sciences, Volume 12 (2010), pp. 20-29

[5] Balan, V.; Brinzei, N. Einstein equations for (h,v) – Berwald–Moor relativistic models, Balkan. J. Geom. Appl., Volume 11 (2006) no. 2, pp. 20-26

[6] Balan, V.; Brinzei, N. Berwald–Moor-type (h,v)-metric physical models, Hypercomplex Numbers in Geometry and Physics, Volume 2 (2005) no. 2(4), pp. 114-122

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

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

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

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