Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties

Najafi, Behzad; Zhang, Shen; Tayebi, A.

doi:10.1007/s10711-007-9218-9

Cited by 56 publications

(40 citation statements)

References 10 publications

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“…They all vanish for Riemannian metrics; hence they are said to be non-Riemannian [6,7,9]. The S-curvature is constructed by Shen for given comparison theorems on Finsler manifolds [10].…”

Section: Introductionmentioning

confidence: 99%

On Finsler metrics with vanishing S-curvature

Tayabi¹,

Sadeghi²,

Peyghan³

2014

Turk J Math

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“…They all vanish for Riemannian metrics; hence they are said to be non-Riemannian [6,7,9]. The S-curvature is constructed by Shen for given comparison theorems on Finsler manifolds [10].…”

Section: Introductionmentioning

confidence: 99%

On Finsler metrics with vanishing S-curvature

Tayabi¹,

Sadeghi²,

Peyghan³

2014

Turk J Math

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“…The H-curvature H y = H ij dx i ⊗ dx j is defined by H ij = E ij|k y k where " | " denote the covariant horizontal derivatives and E ij denote the mean Berwald curvature of F [9,12].…”

Section: Preliminariesmentioning

confidence: 99%

“…In particular, F is said to be of constant flag curvature if the flag curvature K(P, y) = constant [16]. By a basic result of Arbar-Zadeh [1,12] for a Finsler metric of scalar flag curvature, the flag curvature is constant on the manifold if and only if H = 0.…”

Section: Counterexamples To Tang's Theorem 12mentioning

confidence: 99%

On Finsler Metrics of Constant S-Curvature

Mo¹,

Wang²

2013

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we study Finsler metrics of constant S-curvature. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (α, β)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen' construction.

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“…where " | " denotes the covariant horizontal derivatives and E ij denote the mean Berwald curvature of F [8,13]. The H-curvature vanishes for a R-quadratic Finsler metric [7,9].…”

Section: )mentioning

confidence: 99%

A New Quantity in Riemann-Finsler Geometry

Zhang

Liu

2012

Glasgow Math. J.

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Abstract. In this note, we study a new Finslerian quantityĈ defined by the Riemannian curvature. We prove that the new Finslerian quantity is a non-Riemannian quantity for a Finsler manifold with dimension n = 3. Then we study Finsler metrics of scalar curvature. We find that theĈ-curvature is closely related to the flag curvature and the H-curvature. We show thatĈ-curvature gives, a measure of the failure of a Finsler metric to be of weakly isotropic flag curvature. We also give a simple proof of the Najafi-Shen-Tayebi' theorem.1991 Mathematics Subject Classification. 58E20. Recently, a great progress has been made in studying Finsler metrics of weakly isotropic flag curvature. These Finsler metrics are of scalar curvature whose flag curvature is in a special form K = θ/F + σ where θ is a 1-form and σ is a scalar function on M. Finsler metrics of weakly isotropic flag curvature not only include Finsler metrics of constant flag curvature, but also include Finsler metrics of (almost) isotropic S-curvature and of scalar flag curvature [4, 6, 13]. Cheng and Shen have

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Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties

Cited by 56 publications

References 10 publications

On Finsler metrics with vanishing S-curvature

On Finsler metrics with vanishing S-curvature

On Finsler Metrics of Constant S-Curvature

A New Quantity in Riemann-Finsler Geometry

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