On generalized m-th root finsler metrics

Tayebi, A.; Nia, Mohammad Shahbazi; Peyghan, E.

doi:10.1016/j.laa.2012.02.025

Cited by 23 publications

(10 citation statements)

References 13 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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“…In [9], Li-Shen defined the notion of generalized m-th root metrics and studied locally projectively flat generalized fourth root metrics. In [20], Tayebi-Peyghan-Shahbazi consider these metrics and characterize locally dually flat generalized m-th root metrics. If B = 0, then we get…”

Section: Introductionmentioning

confidence: 99%

A new class of projectively flat Finsler metrics with constant flag curvatureK=1

Tayebi

Nia

2015

Differential Geometry and its Applications

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Available online xxxx Communicated by Z. Shen MSC: 53C60 53C25 Keywords: Flag curvature Projectively flat metric Locally dually flat metricIn this paper, we consider a class of Finsler metrics which obtained by Kropina change of the class of generalized m-th root Finsler metrics. We classify projectively flat Finsler metrics in this class of metrics. Then under a condition, we show that every projectively flat Finsler metric in this class with constant flag curvature is locally Minkowskian. Finally, we find necessary and sufficient condition under which this class of metrics be locally dually flat.

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“…. y im with a i1...im symmetric in all its indices [3][8] [9][10] [13]. Then F is called an m-th root Finsler metric.…”

Section: Introductionmentioning

confidence: 99%

On Kropina Change for mth Root Finsler Metrics

2014

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On generalized m-th root finsler metrics

Cited by 23 publications

References 13 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

A new class of projectively flat Finsler metrics with constant flag curvatureK=1

On Kropina Change for mth Root Finsler Metrics

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