On Einstein m-th root metrics

Yu, Y. H.; You, Yong Sung

doi:10.1016/j.difgeo.2009.10.011

Cited by 25 publications

(17 citation statements)

References 3 publications

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“…Y. Yu and Y. You show that an m-th root Einstein Finsler metric is Ricci-flat [9]. The authors characterize locally dually flat m-th root Finsler metrics as well as m-th root y-Berwald metrics in [8].…”

Section: Introductionmentioning

confidence: 97%

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On m-th root metrics with special curvature properties

Tayebi

Najafi

2011

Comptes Rendus. Mathématique

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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.© 2011 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved. r é s u m éDans 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.

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Section: Introductionmentioning

confidence: 97%

“…Proof of the Main TheoremsLemma 3. (See[9].) Let F be an m-th root Finsler metric on an open subset U ⊂ R n .…”

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confidence: 99%

On m-th root metrics with special curvature properties

Tayebi

Najafi

2011

Comptes Rendus. Mathématique

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“…Finsler spaces with rational spray coefficients have been studied in [9]. Further, in [11], it was proved that Einstein m-th root metrics are Ricci flat using the rationality of the Riemann curvature of an 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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“…Y. Yu and Y. You show that an m-th root Einstein Finsler metric is Ricci-flat [14]. In this paper, we have considered a transformation of the more generalized m-th root metric such that it transforms to a similar metric as the generalized Randers one defined in (1.2) in a way that the Finslerian metric F is replaced with more generalized m-th root metric F defined in (1.4).…”

Section: Introductionmentioning

confidence: 99%