Curvature properties of $(\alpha, \beta)$-metrics

Bácsó, Sándor; Cheng, Xinyue; Zhang, Shen

doi:10.2969/aspm/04810073

Cited by 27 publications

(22 citation statements)

References 6 publications

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“…They play an important role in Finsler geometry (see [3]). The important applications of (α, β)-metrics in physics and biology(ecology) have also been found.…”

Section: Preliminarymentioning

confidence: 99%

On conformally flat (\alpha,\beta)-metrics with relatively isotropic mean Landsberg curvature

Cheng¹,

Li²,

Zou³

2014

Publ. Math. Debrecen

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In this paper, we study conformally flat (α, β)-metrics in the form of F = αφ(β/α), where α is a Riemannian metric and β is a 1-form on the manifold. We prove that conformally flat weak Landsberg (α, β)-metrics must be either Riemannian metrics or locally Minkowski metrics. Further, we prove that, if φ(s) is a polynomial in s, then conformally flat (α, β)-metrics with relatively isotropic mean Landsberg curvature must also be either Riemannian metrics or locally Minkowski metrics.Mathematics Subject Classification: 53B40, 53C60.

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“…They play an important role in Finsler geometry (see [3]). The important applications of (α, β)-metrics in physics and biology(ecology) have also been found.…”

Section: Preliminarymentioning

confidence: 99%

On conformally flat (\alpha,\beta)-metrics with relatively isotropic mean Landsberg curvature

Cheng¹,

Li²,

Zou³

2014

Publ. Math. Debrecen

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“…Proof Firstly we have that if (M, F ) has constant flag curvature, then (M, h) has constant sectional curvature (see [1]). Let f be the first Dirichlet eigenfunction corresponding to the first eigenvalue λ 1 in Ω, that is,…”

Section: The Lower Bound Estimation Of the First Eigenvaluementioning

confidence: 99%

Eigenvalue comparison theorems on Finsler manifolds

Yin

2014

Chin. Ann. Math. Ser. B

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“…This class of metrics was first introduced by Matsumoto which appear iteratively in formulating physics, mechanics, biology and ecology, etc [1,8]. An (α, β)-metric is a Finsler metric of the form F := αφ(s),…”

Section: Introductionmentioning

confidence: 99%

On generalized Douglas–Weyl (α, β)-metrics

Tayebi

Sadeghi

2015

Acta. Math. Sin.-English Ser.

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In this paper, we study generalized Douglas-Weyl (α, β)-metrics. Suppose that a regular (α, β)-metric F is not of Randers type. We prove that F is a generalized Douglas-Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas-Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.

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Curvature properties of $(\alpha, \beta)$-metrics

Cited by 27 publications

References 6 publications

On conformally flat (\alpha,\beta)-metrics with relatively isotropic mean Landsberg curvature

On conformally flat (\alpha,\beta)-metrics with relatively isotropic mean Landsberg curvature

Eigenvalue comparison theorems on Finsler manifolds

On generalized Douglas–Weyl (α, β)-metrics

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