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

@article{CRMATH_2011__349_11-12_691_0,
     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},
     publisher = {Elsevier},
     volume = {349},
     number = {11-12},
     year = {2011},
     doi = {10.1016/j.crma.2011.06.004},
     language = {en},
}

TY  - JOUR
AU  - Akbar Tayebi
AU  - Behzad Najafi
TI  - On m-th root metrics with special curvature properties
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 691
EP  - 693
VL  - 349
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crma.2011.06.004
LA  - en
ID  - CRMATH_2011__349_11-12_691_0
ER  -

%0 Journal Article
%A Akbar Tayebi
%A Behzad Najafi
%T On m-th root metrics with special curvature properties
%J Comptes Rendus. Mathématique
%D 2011
%P 691-693
%V 349
%N 11-12
%I Elsevier
%R 10.1016/j.crma.2011.06.004
%G en
%F CRMATH_2011__349_11-12_691_0

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

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

[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

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

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

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

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

[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

Chang Tian; Yong He; Weina Lu; Jiayidaer Eryzabk On some non-Riemannian curvature of Minkowskian product Finsler metrics, Journal of Mathematical Analysis and Applications, Volume 534 (2024) no. 2, p. 128070 | DOI:10.1016/j.jmaa.2023.128070
Jila Majidi; Akbar Tayebi; Ali Haji-Badali On Einstein-reversible mth root Finsler metrics, International Journal of Geometric Methods in Modern Physics, Volume 20 (2023) no. 06 | DOI:10.1142/s0219887823500998
Patrícia Carvalho; Cristian Landri; Ravi Mistry; Aleksandr Pinzul Multimetric Finsler geometry, International Journal of Modern Physics A, Volume 38 (2023) no. 03 | DOI:10.1142/s0217751x23500185
A. Tayebi; M. Razgordani; B. Najafi On Conformally Flat Cubic (α,β )-Metrics, Vietnam Journal of Mathematics, Volume 49 (2021) no. 4, p. 987 | DOI:10.1007/s10013-020-00389-0
Akbar Tayebi On 4-th root metrics of isotropic scalar curvature, Mathematica Slovaca, Volume 70 (2020) no. 1, p. 161 | DOI:10.1515/ms-2017-0341
A. Tayebi; M. Razgordani On conformally flat fourth root (α,β)-metrics, Differential Geometry and its Applications, Volume 62 (2019), p. 253 | DOI:10.1016/j.difgeo.2018.12.002
Akbar Tayebi On the theory of $4$ -th root Finsler metrics, Tbilisi Mathematical Journal, Volume 12 (2019) no. 1 | DOI:10.32513/tbilisi/1553565628
T. R. Khoshdani; N. Abazari Characterization of Weakly Berwald Fourth-Root Metrics, Ukrainian Mathematical Journal, Volume 71 (2019) no. 7, p. 1115 | DOI:10.1007/s11253-019-01702-y
Akbar Tayebi On generalized 4-th root metrics of isotropic scalar curvature, Mathematica Slovaca, Volume 68 (2018) no. 4, p. 907 | DOI:10.1515/ms-2017-0154
A. Tayebi; M. Razgordani Four families of projectively flat Finsler metrics with $K = 1$ K = 1 and their non-Riemannian curvature properties, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Volume 112 (2018) no. 4, p. 1463 | DOI:10.1007/s13398-017-0443-2
A. Tayebi; A. Nankali; E. Peyghan Some properties of m-th root Finsler metrics, Journal of Contemporary Mathematical Analysis, Volume 49 (2014) no. 4, p. 184 | DOI:10.3103/s1068362314040049
Akbar Tayebi; Ali Nankali; Esmaeil Peyghan Some curvature properties of Cartan spaces with mth root metrics, Lithuanian Mathematical Journal, Volume 54 (2014) no. 1, p. 106 | DOI:10.1007/s10986-014-9230-3
A. Tayebi; T. Tabatabaeifar; E. Peyghan On Kropina Change for mth Root Finsler Metrics, Ukrainian Mathematical Journal, Volume 66 (2014) no. 1, p. 160 | DOI:10.1007/s11253-014-0919-6
Esmaeil Peyghan WITHDRAWN: About R-quadratic Finsler metrics, Comptes Rendus Mathematique (2012) | DOI:10.1016/j.crma.2012.04.018
A. Tayebi; E. Peyghan On a subclass of the class of generalized Douglas-Weyl metrics, Journal of Contemporary Mathematical Analysis, Volume 47 (2012) no. 2, p. 70 | DOI:10.3103/s1068362312020033
Akbar Tayebi; Mohammad Shahbazi Nia; Esmaeil Peyghan On generalized m-th root finsler metrics, Linear Algebra and its Applications, Volume 437 (2012) no. 2, p. 675 | DOI:10.1016/j.laa.2012.02.025

Cité par 16 documents. Sources : Crossref

Commentaires - Politique