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arXiv · 1510.07990

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

A. Tayebi·H. Sadeghi
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Abstract

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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BibTeXRIS

A. Tayebi, H. Sadeghi. 2015-10-26. On Generalized Douglas-Weyl $(α, β)$-Metrics. https://doi.org/10.1007/s10114-015-3418-2

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