On Generalized Kropina Change of Generalized m-th Root Finsler Metrics

Tiwari, Bankteshwar; Kumar, Manoj; Tayebi, A.

doi:10.1007/s40010-020-00681-1

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…A. Tayebi et al [12] and Bankteswar Tiwari et al [13] discussed the Kropina change and generalized Kropina change respectively, for the Finsler space with m th root metric. In 2017, A. Tayebi et al [11] obtained the condition for the Finsler space given by Matsumoto change to be projectively related with the original Finsler space.…”

Section: Introductionmentioning

confidence: 99%

Cartan Connection for h-Matsumoto change

Gupta¹,

Sahu²,

Sharma³

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

Cartan Connection for h-Matsumoto change

Gupta¹,

Sahu²,

Sharma³

2022

Preprint

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“…Also, Matsumoto studied two-dimensional cubic metrics and based on the main scalar, he found the necessary and sufficient condition under which a Finsler metric be a cubic metric. For more progress on m-th root Finsler metrics one can see [14]- [21] and [23]- [26].…”

Section: Introductionmentioning

confidence: 99%

ON CUBIC (\alpha, \beta)-METRICS IN FINSLER GEOMETRY

Vishkaei

Tayebi²

2022

FU Math Inform

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“…Namely, the generalized Kropina metric, the m-th root metric cf. [11], the Kropina change of the m-th root metric and the generalized Kropina change of the m-th root metric [7,8]. Besides, we introduce a new Finsler metric looks like the m-th root metric but its coefficients are functions on T M rather than functions on M, as in the case of m-th root metric, which we refer to as extended m-th root metric.…”

Section: Introductionmentioning

confidence: 99%

On almost rational Finsler metrics

Taha¹,

Tiwari²

2021

Preprint

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We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and sufficient conditions for an AR-Finsler manifold (M, F ) to be Riemannian. The rationality of the associated geometric objects such as Cartan torsion, geodesic spray, Landsberg curvature, S-curvature, etc is investigated. We prove for a particular subset of AR-Finsler metrics that if F has isotropic S-curvature, then its S-curvature identically vanishes. Further, if F has isotropic mean Landsberg curvature, then it is weakly Landsberg. Also, if F is an Einstein metric, then it is Ricci-flat. Moreover, we show that Randers metric can not be AR-Finsler metric. Finally, we provide some examples of AR-Finsler metrics and introduce a new Finsler metric which is called an extended m-th root metric. We show under what conditions an extended m-th root metric is AR-Finsler metric and study its generalized Kropina change.

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On Generalized Kropina Change of Generalized m-th Root Finsler Metrics

Cited by 5 publications

References 14 publications

Cartan Connection for h-Matsumoto change

Cartan Connection for h-Matsumoto change

ON CUBIC (\alpha, \beta)-METRICS IN FINSLER GEOMETRY

On almost rational Finsler metrics

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