Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 43-52.

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A Note on Generalized Douglas-Weyl Spray

Zheng Daxiao()   

  1. Department of Mathematics and Statistics Science, Anhui Normal University, Anhui Wuhu 241002
  • Received:2022-03-07 Revised:2022-07-22 Online:2023-02-26 Published:2023-03-07
  • Supported by:
    The AHNSF(2008085QA05)


In this paper, we study Generalized Douglas-Weyl spray. We show that a spray $G$ is a Generalized Douglas-Weyl spray if and only if it is $W$-quadratic. As a corollary, we show that a Finsler metric $F$ is a Generalized Douglas-Weyl metric if and only if it is $W$-quadratic. Furthermore, we consider $R$-quadratic spray and prove that a spray $G$ is $R$-quadratic if and only if $\dot{B}^{~i}_{j~kl}=0$.

Key words: Spray, Weyl curvature, Douglas Tensor

CLC Number: 

  • O184