Some properties of m-th root Finsler metrics

Tayebi, A.; Nankali, Ali; Peyghan, E.

doi:10.3103/s1068362314040049

Cited by 4 publications

(1 citation statement)

References 15 publications

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“…Tiwari and Kumar [16] studied the Randers change of a Finsler space with mth root metric. Tayebi et al [11][12][13] studied the mth root Finsler metric with several non-Riemannian quantities of Berwald curvature, Landsberg curvature, H-curvature, etc., and they established a necessary and sufficient condition to be projectively flat and locally dually flat for Kropina change of m th root metrics [15]. Xu and Li [17] …”

Section: Introductionmentioning

confidence: 99%

On generalized Kropina change of $m$th root Finsler metrics with special curvature properties

Tiwari¹,

Prajapati²

2017

Turk J Math

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In the present paper, we consider generalized Kropina change of m th root Finsler metrics and prove that every generalized Kropina change of m th root Finsler metrics with isotropic Berwald curvature, isotropic mean Berwald curvature, relatively isotropic Landsberg curvature, and relatively isotropic mean Landsberg curvature reduces to the Berwald metric, weakly Berwald metric, Landsberg metric, and weakly Landsberg metric, respectively. We also show that every generalized Kropina change of m th root Finsler metrics with almost vanishing H -curvature has vanishing H -curvature.

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Section: Introductionmentioning

confidence: 99%

On generalized Kropina change of $m$th root Finsler metrics with special curvature properties

Tiwari¹,

Prajapati²

2017

Turk J Math

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On Conformally Flat Cubic (α,β )-Metrics

2020

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On generalized 4-th root metrics of isotropic scalar curvature

Tayebi

2018

Mathematica Slovaca

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By an interesting physical perspective and a suitable contraction of the Riemannian curvature tensor in Finsler geometry, Akbar-Zadeh introduced the notion of scalar curvature for the Finsler metrics. A Finsler metric is called of isotropic scalar curvature if the scalar curvature depends on the position only. In this paper, we study the class of generalized 4-th root metrics. These metrics generalize 4-th root metrics which are used in Biology as ecological metrics. We find the necessary and sufficient condition under which a generalized 4-th root metric is of isotropic scalar curvature. Then, we find the necessary and sufficient condition under which the conformal change of a generalized 4-th root metric is of isotropic scalar curvature. Finally, we characterize the Bryant metrics of isotropic scalar curvature.

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Some properties of m-th root Finsler metrics

Cited by 4 publications

References 15 publications

On generalized Kropina change of $m$th root Finsler metrics with special curvature properties

On generalized Kropina change of $m$th root Finsler metrics with special curvature properties

On Conformally Flat Cubic (α,β )-Metrics

On generalized 4-th root metrics of isotropic scalar curvature

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