A note on a generalized Douglas space

Bácsó, Sándor; Papp, Ildikó

doi:10.1023/b:mahu.0000038974.24588.83

Cited by 20 publications

(11 citation statements)

References 6 publications

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“…There are some well-known projective invariants of Finsler metrics namely Douglas curvature, Weyl curvature [2], generalized Douglas-Weyl curvature [3], and another projective invariant by Akbar-Zadeh [1] (For another special projective invariant, see [15,19]). Recently, Z. Shen [17] defined the concept of projective Ricci curvature PRic for a Finsler metric F as…”

Section: Introductionmentioning

confidence: 99%

On isotropic projective Ricci curvature of C-reducible Finsler metrics

Ghaemnezhad¹,

Rezaei²,

Gabrani³

2019

Turk J Math

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Projective Ricci curvature is a projective invariant quantity in Finsler geometry which is introduced by Z. Shen. In this paper, we study special projective Ricci curvature of C-reducible Finsler metrics. The necessary and sufficient conditions of these metrics, which cause these metrics to be weak or isotropic projective Ricci curvature, are found and it is proved that C-reducible Douglas metric of isotropic PRic-curvature must be PRic flat. The same theorem for C-reducible metrics of scalar flag curvature is also investigated.

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Section: Introductionmentioning

confidence: 99%

On isotropic projective Ricci curvature of C-reducible Finsler metrics

Ghaemnezhad¹,

Rezaei²,

Gabrani³

2019

Turk J Math

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“…In [3], Bácsó-Papp showed that GDW (M ) is closed under projective changes. Then, NajafiShen-Tayebi characterized generalized Douglas-Weyl Randers metrics [10].…”

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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“…For a manifold M , let GDW (M ) denotes the class of all Finsler metrics satisfying in above relation for some tensor T jkl . In [3], Bácsó-Papp showed that GDW (M ) is closed under projective changes. Then, Najafi-Shen-Tayebi characterized generalized Douglas-Weyl Randers metrics [10].…”

Section: Introductionmentioning

confidence: 99%

On Generalized Douglas-Weyl $(α, β)$-Metrics

Tayebi,

Sadeghi

2015

Preprint

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In this paper, we study generalized Douglas-Weyl (α, β)-metrics. Suppose that an 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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A note on a generalized Douglas space

Cited by 20 publications

References 6 publications

On isotropic projective Ricci curvature of C-reducible Finsler metrics

On isotropic projective Ricci curvature of C-reducible Finsler metrics

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

On Generalized Douglas-Weyl $(α, β)$-Metrics

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