On generalized Douglas–Weyl (α, β)-metrics
On generalized Douglas–Weyl (α, β)-metrics
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DOI：
10.1007/s10114-015-3418-2
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发表时间：
2015-09
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影响因子：
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通讯作者：
A. Tayebi;H. Sadeghi
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文献类型：
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作者：
A. Tayebi;H. Sadeghi
本文研究了广义Douglas-Weyl (α,β)-度量。假设一个正则(α,β)- metricfi不是Randers类型。我们证明了f是一个s曲率消失的广义道格拉斯-魏尔度规当且仅当它是一个伯瓦尔德度规。此外，通过忽略规律性，如果f不是伯瓦尔德度规，那么我们就会发现一个几乎规则的芬斯勒度规族，它既不是道格拉斯也不是Weyl。作为其应用，我们证明了具有各向同性平均伯瓦尔德曲率的广义Douglas-Weyl平方度规和Matsumoto度规都是伯瓦尔德度规。
In this paper, we study generalized Douglas–Weyl (α,β)-metrics. Suppose that a regular (α,β)-metricFis not of Randers type. We prove thatFis a generalized Douglas–Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, ifFis 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.