Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (6): 1831-1842.

Previous Articles     Next Articles

Landsberg Finsler Warped Product Metrics with Zero Flag Curvature

Zheng Daxiao()   

  1. Department of Mathematics and Statistics Science, Anhui Normal University, Anhui Wuhu 241002
  • Received:2022-08-30 Revised:2022-12-30 Online:2023-12-26 Published:2023-11-16
  • Supported by:
    Anhui Provincial Natural Science Youth Foundation(2008085QA05)

Abstract:

In this paper, we study Finsler warped product metrics. We obtain the differential equations that characterize Landsberg Finsler warped product metrics. By solving these equations, we obtain the expression of these metrics. Furthermore, we construct a class of Finsler warped product metrics $F$ with the following properties: $(1)$ $F$ is a Landsberg metric; $(2)$ $F$ is not a Berwald metric; $(3)$ $F$ has zero flag curvature (or Ricci curvature).

Key words: Finsler warped product metrics, Douglas metrics, Flag curvature, Landsberg

CLC Number: 

  • O184
Trendmd