On Generalized Douglas-Weyl $(\alpha, \beta)$-Metrics

摘要

In this paper, we study generalized Douglas-Weyl $(\alpha, \beta)$-metrics.Suppose that an regular $(\alpha, \beta)$-metric $F$ is not of Randers type. Weprove that $F$ is a generalized Douglas-Weyl metric with vanishing S-curvatureif 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 Finslermetrics which is not Douglas nor Weyl. As its application, we show thatgeneralized Douglas-Weyl square metric or Matsumoto metric with isotropic meanBerwald curvature are Berwald metrics.