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

作　　者：Akbar TAYEBI Hassan SADEGHI 

机构地区：[1]Department of Mathematics, Faculty of Science, University of Qom

出　　处：《Acta Mathematica Sinica,English Series》2015年第10期1611-1620,共10页数学学报（英文版）

摘　　要：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.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.

关 键 词：Generalized Douglas Weyl metric Weyl metric Douglas metric S-CURVATURE 

分 类 号：O186.11[理学—数学]